Galois representations in arithmetic algebraic geometry /:
This book contains conference proceedings from the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic g...
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
1998.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
254. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book contains conference proceedings from the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and contains a mixture of articles. Some are expositions of subjects which have received substantial attention, e.g. Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties in mixed characteristics; Rubin and Scholl on the work of Kato on the Birch-Swinnerton-Dyer conjecture; and Schneider on rigid geometry. Others are research papers by authors such as Coleman and Mazur, Goncharov, Gross and Serre. |
| Beschreibung: | 1 online resource (493 pages) |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781107362727 1107362725 9780511662010 0511662017 |
Internformat
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 254 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book contains conference proceedings from the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and contains a mixture of articles. Some are expositions of subjects which have received substantial attention, e.g. Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties in mixed characteristics; Rubin and Scholl on the work of Kato on the Birch-Swinnerton-Dyer conjecture; and Schneider on rigid geometry. Others are research papers by authors such as Coleman and Mazur, Goncharov, Gross and Serre. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; List of Participants; Lecture programme; The Eigencurve; Chapter 1. Rigid analytic varieties.; 1.1 Rigid analytic spaces attached to complete local noetherianrings.; 1.2. Irreducible components and component parts.; 1.3. Fredholm varieties.; 1.4 Weight space.; 1.5. The eigencurve as the Fredholm closure of the classical modularlocus. (Statement of the main theorems); Chapter 2. Modular Forms.; 2.1 Affinoid sub-domains in modular curves.; 2.2 Eisenstein series.; 2.3. Katz p-adic Modular Functions. | |
| 505 | 8 | |a 2.4 Convergent modular forms and Katz modular functions. Chapter 3. Hecke Algebras; 3.1 Hecke eigenvectors and generalized eigenvectors.; 3.2. Action on Mk; 3.3 Action on Katz Modular Functions.; 3.4. Action on Mt(N).; 3.5. Action on weight K forms.; 3.6. Remarks about cusp forms and Eisenstein series.; Chapter 4. Fredholm determinants.; 4.1. Completely continuous operators and Fredholm determinants; 4.2. Factoring Characteristic Series.; 4.3. Analytic variation of the Fredholm determinant.; 4.4 The Spectral Curves.; Chapter 5. Galois representations and pseudo-representations. | |
| 505 | 8 | |a 5.1. Deforming representations and pseudo-representations. 5.2. Pseudo-representations attached to Katz modular functions.; Chapter 6. The Eigencurve.; 6.1. The definition of the eigencurve.; 6.2. The points of the eigencurve are overconvergent eigenforms.; 6.3. The projections of the eigencurve to the spectral curves.; 6.4. The Eisenstein curve.; Chapter 7. The eigencurve as a finite cover of a spectral curve.; 7.1. Local pieces.; 7.2. Gluing.; 7.3. The relationships among the curves; 7.4. D is reduced.; 7.5. Equality of D and C; 7.6. Consequences of the relationship between D and C. | |
| 505 | 8 | |a 7 Equivariant motivesReferences; Mixed elliptic motives; 1 Introduction; 2 Two basic examples: a survey; 3 Mixed motives and motivic Lie algebras; 4 Conjectures on the motivic Galois group; 5 Towards the Lie coalgebra; 6 Reflections on elliptic motivic complexes; 7 The complexes; 8 The regulator integrals, Eisenstein-Kroneckerseries and a conjecture on; 9 The complexes B(E; n).and motivic elliptic polylogarithms; 10 Elliptic Chow polylogarithms and generalized Eisenstein-Kronecker series; REFERENCES; On the Satake isomorphism; 1. The algebraic group; 2. The Gelfand pair (G, K) | |
| 650 | 0 | |a Arithmetical algebraic geometry |v Congresses. | |
| 650 | 0 | |a Algebraic number theory |v Congresses. | |
| 650 | 0 | |a Galois theory |v Congresses. | |
| 650 | 6 | |a Géométrie algébrique arithmétique |v Congrès. | |
| 650 | 6 | |a Théorie algébrique des nombres |v Congrès. | |
| 650 | 6 | |a Théorie de Galois |v Congrès. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
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| 700 | 1 | |a Scholl, A. J. |q (Anthony James), |d 1955- |1 https://id.oclc.org/worldcat/entity/E39PBJkMDPGjrTVmJKhMC9pMfq |0 http://id.loc.gov/authorities/names/n98072742 | |
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| contents | Cover; Title; Copyright; Contents; Preface; List of Participants; Lecture programme; The Eigencurve; Chapter 1. Rigid analytic varieties.; 1.1 Rigid analytic spaces attached to complete local noetherianrings.; 1.2. Irreducible components and component parts.; 1.3. Fredholm varieties.; 1.4 Weight space.; 1.5. The eigencurve as the Fredholm closure of the classical modularlocus. (Statement of the main theorems); Chapter 2. Modular Forms.; 2.1 Affinoid sub-domains in modular curves.; 2.2 Eisenstein series.; 2.3. Katz p-adic Modular Functions. 2.4 Convergent modular forms and Katz modular functions. Chapter 3. Hecke Algebras; 3.1 Hecke eigenvectors and generalized eigenvectors.; 3.2. Action on Mk; 3.3 Action on Katz Modular Functions.; 3.4. Action on Mt(N).; 3.5. Action on weight K forms.; 3.6. Remarks about cusp forms and Eisenstein series.; Chapter 4. Fredholm determinants.; 4.1. Completely continuous operators and Fredholm determinants; 4.2. Factoring Characteristic Series.; 4.3. Analytic variation of the Fredholm determinant.; 4.4 The Spectral Curves.; Chapter 5. Galois representations and pseudo-representations. 5.1. Deforming representations and pseudo-representations. 5.2. Pseudo-representations attached to Katz modular functions.; Chapter 6. The Eigencurve.; 6.1. The definition of the eigencurve.; 6.2. The points of the eigencurve are overconvergent eigenforms.; 6.3. The projections of the eigencurve to the spectral curves.; 6.4. The Eisenstein curve.; Chapter 7. The eigencurve as a finite cover of a spectral curve.; 7.1. Local pieces.; 7.2. Gluing.; 7.3. The relationships among the curves; 7.4. D is reduced.; 7.5. Equality of D and C; 7.6. Consequences of the relationship between D and C. 7 Equivariant motivesReferences; Mixed elliptic motives; 1 Introduction; 2 Two basic examples: a survey; 3 Mixed motives and motivic Lie algebras; 4 Conjectures on the motivic Galois group; 5 Towards the Lie coalgebra; 6 Reflections on elliptic motivic complexes; 7 The complexes; 8 The regulator integrals, Eisenstein-Kroneckerseries and a conjecture on; 9 The complexes B(E; n).and motivic elliptic polylogarithms; 10 Elliptic Chow polylogarithms and generalized Eisenstein-Kronecker series; REFERENCES; On the Satake isomorphism; 1. The algebraic group; 2. The Gelfand pair (G, K) |
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| discipline | Mathematik |
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| genre | Conference papers and proceedings fast |
| genre_facet | Conference papers and proceedings |
| id | ZDB-4-EBA-ocn836871693 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107362727 1107362725 9780511662010 0511662017 |
| language | English |
| oclc_num | 836871693 |
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| physical | 1 online resource (493 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1998 |
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| publisher | Cambridge University Press, |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Galois representations in arithmetic algebraic geometry / edited by A.J. Scholl, R.L. Taylor. New York : Cambridge University Press, 1998. 1 online resource (493 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 254 Includes bibliographical references. Print version record. This book contains conference proceedings from the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and contains a mixture of articles. Some are expositions of subjects which have received substantial attention, e.g. Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties in mixed characteristics; Rubin and Scholl on the work of Kato on the Birch-Swinnerton-Dyer conjecture; and Schneider on rigid geometry. Others are research papers by authors such as Coleman and Mazur, Goncharov, Gross and Serre. Cover; Title; Copyright; Contents; Preface; List of Participants; Lecture programme; The Eigencurve; Chapter 1. Rigid analytic varieties.; 1.1 Rigid analytic spaces attached to complete local noetherianrings.; 1.2. Irreducible components and component parts.; 1.3. Fredholm varieties.; 1.4 Weight space.; 1.5. The eigencurve as the Fredholm closure of the classical modularlocus. (Statement of the main theorems); Chapter 2. Modular Forms.; 2.1 Affinoid sub-domains in modular curves.; 2.2 Eisenstein series.; 2.3. Katz p-adic Modular Functions. 2.4 Convergent modular forms and Katz modular functions. Chapter 3. Hecke Algebras; 3.1 Hecke eigenvectors and generalized eigenvectors.; 3.2. Action on Mk; 3.3 Action on Katz Modular Functions.; 3.4. Action on Mt(N).; 3.5. Action on weight K forms.; 3.6. Remarks about cusp forms and Eisenstein series.; Chapter 4. Fredholm determinants.; 4.1. Completely continuous operators and Fredholm determinants; 4.2. Factoring Characteristic Series.; 4.3. Analytic variation of the Fredholm determinant.; 4.4 The Spectral Curves.; Chapter 5. Galois representations and pseudo-representations. 5.1. Deforming representations and pseudo-representations. 5.2. Pseudo-representations attached to Katz modular functions.; Chapter 6. The Eigencurve.; 6.1. The definition of the eigencurve.; 6.2. The points of the eigencurve are overconvergent eigenforms.; 6.3. The projections of the eigencurve to the spectral curves.; 6.4. The Eisenstein curve.; Chapter 7. The eigencurve as a finite cover of a spectral curve.; 7.1. Local pieces.; 7.2. Gluing.; 7.3. The relationships among the curves; 7.4. D is reduced.; 7.5. Equality of D and C; 7.6. Consequences of the relationship between D and C. 7 Equivariant motivesReferences; Mixed elliptic motives; 1 Introduction; 2 Two basic examples: a survey; 3 Mixed motives and motivic Lie algebras; 4 Conjectures on the motivic Galois group; 5 Towards the Lie coalgebra; 6 Reflections on elliptic motivic complexes; 7 The complexes; 8 The regulator integrals, Eisenstein-Kroneckerseries and a conjecture on; 9 The complexes B(E; n).and motivic elliptic polylogarithms; 10 Elliptic Chow polylogarithms and generalized Eisenstein-Kronecker series; REFERENCES; On the Satake isomorphism; 1. The algebraic group; 2. The Gelfand pair (G, K) Arithmetical algebraic geometry Congresses. Algebraic number theory Congresses. Galois theory Congresses. Géométrie algébrique arithmétique Congrès. Théorie algébrique des nombres Congrès. Théorie de Galois Congrès. MATHEMATICS Geometry Algebraic. bisacsh Algebraic number theory fast Arithmetical algebraic geometry fast Galois theory fast Arithmetische Geometrie gnd http://d-nb.info/gnd/4131383-5 Galois-Darstellung gnd http://d-nb.info/gnd/4221407-5 Algebraïsche meetkunde. gtt Galois-theorie. gtt Géométrie algébrique arithmétique Congrès. ram Nombres algébriques, Théorie des Congrès. ram Galois, Théorie de Congrès. ram Conference papers and proceedings fast Scholl, A. J. (Anthony James), 1955- https://id.oclc.org/worldcat/entity/E39PBJkMDPGjrTVmJKhMC9pMfq http://id.loc.gov/authorities/names/n98072742 Taylor, R. L. (Richard Lawrence), 1962- http://id.loc.gov/authorities/names/nb2012018027 has work: Galois representations in arithmetic algebraic geometry (Work) https://id.oclc.org/worldcat/entity/E39PCG3M6hVt4wcRGMDmbRVt8C https://id.oclc.org/worldcat/ontology/hasWork Print version: Galois representations in arithmetic algebraic geometry. New York : Cambridge University Press, 1998 0521644194 (DLC) 98041632 (OCoLC)39727652 London Mathematical Society lecture note series ; 254. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552447 Volltext |
| spellingShingle | Galois representations in arithmetic algebraic geometry / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; List of Participants; Lecture programme; The Eigencurve; Chapter 1. Rigid analytic varieties.; 1.1 Rigid analytic spaces attached to complete local noetherianrings.; 1.2. Irreducible components and component parts.; 1.3. Fredholm varieties.; 1.4 Weight space.; 1.5. The eigencurve as the Fredholm closure of the classical modularlocus. (Statement of the main theorems); Chapter 2. Modular Forms.; 2.1 Affinoid sub-domains in modular curves.; 2.2 Eisenstein series.; 2.3. Katz p-adic Modular Functions. 2.4 Convergent modular forms and Katz modular functions. Chapter 3. Hecke Algebras; 3.1 Hecke eigenvectors and generalized eigenvectors.; 3.2. Action on Mk; 3.3 Action on Katz Modular Functions.; 3.4. Action on Mt(N).; 3.5. Action on weight K forms.; 3.6. Remarks about cusp forms and Eisenstein series.; Chapter 4. Fredholm determinants.; 4.1. Completely continuous operators and Fredholm determinants; 4.2. Factoring Characteristic Series.; 4.3. Analytic variation of the Fredholm determinant.; 4.4 The Spectral Curves.; Chapter 5. Galois representations and pseudo-representations. 5.1. Deforming representations and pseudo-representations. 5.2. Pseudo-representations attached to Katz modular functions.; Chapter 6. The Eigencurve.; 6.1. The definition of the eigencurve.; 6.2. The points of the eigencurve are overconvergent eigenforms.; 6.3. The projections of the eigencurve to the spectral curves.; 6.4. The Eisenstein curve.; Chapter 7. The eigencurve as a finite cover of a spectral curve.; 7.1. Local pieces.; 7.2. Gluing.; 7.3. The relationships among the curves; 7.4. D is reduced.; 7.5. Equality of D and C; 7.6. Consequences of the relationship between D and C. 7 Equivariant motivesReferences; Mixed elliptic motives; 1 Introduction; 2 Two basic examples: a survey; 3 Mixed motives and motivic Lie algebras; 4 Conjectures on the motivic Galois group; 5 Towards the Lie coalgebra; 6 Reflections on elliptic motivic complexes; 7 The complexes; 8 The regulator integrals, Eisenstein-Kroneckerseries and a conjecture on; 9 The complexes B(E; n).and motivic elliptic polylogarithms; 10 Elliptic Chow polylogarithms and generalized Eisenstein-Kronecker series; REFERENCES; On the Satake isomorphism; 1. The algebraic group; 2. The Gelfand pair (G, K) Arithmetical algebraic geometry Congresses. Algebraic number theory Congresses. Galois theory Congresses. Géométrie algébrique arithmétique Congrès. Théorie algébrique des nombres Congrès. Théorie de Galois Congrès. MATHEMATICS Geometry Algebraic. bisacsh Algebraic number theory fast Arithmetical algebraic geometry fast Galois theory fast Arithmetische Geometrie gnd http://d-nb.info/gnd/4131383-5 Galois-Darstellung gnd http://d-nb.info/gnd/4221407-5 Algebraïsche meetkunde. gtt Galois-theorie. gtt Géométrie algébrique arithmétique Congrès. ram Nombres algébriques, Théorie des Congrès. ram Galois, Théorie de Congrès. ram |
| subject_GND | http://d-nb.info/gnd/4131383-5 http://d-nb.info/gnd/4221407-5 |
| title | Galois representations in arithmetic algebraic geometry / |
| title_auth | Galois representations in arithmetic algebraic geometry / |
| title_exact_search | Galois representations in arithmetic algebraic geometry / |
| title_full | Galois representations in arithmetic algebraic geometry / edited by A.J. Scholl, R.L. Taylor. |
| title_fullStr | Galois representations in arithmetic algebraic geometry / edited by A.J. Scholl, R.L. Taylor. |
| title_full_unstemmed | Galois representations in arithmetic algebraic geometry / edited by A.J. Scholl, R.L. Taylor. |
| title_short | Galois representations in arithmetic algebraic geometry / |
| title_sort | galois representations in arithmetic algebraic geometry |
| topic | Arithmetical algebraic geometry Congresses. Algebraic number theory Congresses. Galois theory Congresses. Géométrie algébrique arithmétique Congrès. Théorie algébrique des nombres Congrès. Théorie de Galois Congrès. MATHEMATICS Geometry Algebraic. bisacsh Algebraic number theory fast Arithmetical algebraic geometry fast Galois theory fast Arithmetische Geometrie gnd http://d-nb.info/gnd/4131383-5 Galois-Darstellung gnd http://d-nb.info/gnd/4221407-5 Algebraïsche meetkunde. gtt Galois-theorie. gtt Géométrie algébrique arithmétique Congrès. ram Nombres algébriques, Théorie des Congrès. ram Galois, Théorie de Congrès. ram |
| topic_facet | Arithmetical algebraic geometry Congresses. Algebraic number theory Congresses. Galois theory Congresses. Géométrie algébrique arithmétique Congrès. Théorie algébrique des nombres Congrès. Théorie de Galois Congrès. MATHEMATICS Geometry Algebraic. Algebraic number theory Arithmetical algebraic geometry Galois theory Arithmetische Geometrie Galois-Darstellung Algebraïsche meetkunde. Galois-theorie. Nombres algébriques, Théorie des Congrès. Galois, Théorie de Congrès. Conference papers and proceedings |
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