Non-abelian Fundamental Groups and Iwasawa Theory.:
Displays the intricate interplay between different foundations of non-commutative number theory.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , , , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2011.
|
| Schriftenreihe: | London Mathematical Society lecture note series.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Displays the intricate interplay between different foundations of non-commutative number theory. |
| Beschreibung: | 1 online resource (322 pages) |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781139221580 1139221582 9786613580474 6613580473 9781139225014 1139225014 1139218492 9781139218498 9780511984440 0511984448 |
Internformat
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| 100 | 1 | |a Coates, John. | |
| 245 | 1 | 0 | |a Non-abelian Fundamental Groups and Iwasawa Theory. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (322 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a London Mathematical Society Lecture Note Series | |
| 588 | 0 | |a Print version record. | |
| 520 | |a Displays the intricate interplay between different foundations of non-commutative number theory. | ||
| 505 | 0 | |6 880-01 |a Cover; LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES; Title; Copyright; Contents; Contributors; Preface; Lectures on anabelian phenomena in geometry and arithmetic; Part I. Introduction and motivation; A. First examples; B. Galois characterization of global fields; Part II. Grothendieck's anabelian geometry; A. Warm-up: birational anabelian conjectures; B. Anabelian conjectures for curves; C. The section conjectures; Part III. Beyond the arithmetical action; A. Small Galois groups and valuations; B. Variation of fundamental groups in families of curves. | |
| 504 | |a Includes bibliographical references. | ||
| 650 | 0 | |a Iwasawa theory. |0 http://id.loc.gov/authorities/subjects/sh2002004431 | |
| 650 | 0 | |a Non-Abelian groups. |0 http://id.loc.gov/authorities/subjects/sh85092216 | |
| 650 | 4 | |a Iwasawa theory. | |
| 650 | 4 | |a Non-Abelian groups. | |
| 650 | 6 | |a Théorie d'Iwasawa. | |
| 650 | 6 | |a Groupes non abéliens. | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 650 | 7 | |a Iwasawa theory |2 fast | |
| 650 | 7 | |a Non-Abelian groups |2 fast | |
| 650 | 7 | |a Aufsatzsammlung |2 gnd | |
| 650 | 7 | |a Iwasawa-Theorie |2 gnd |0 http://d-nb.info/gnd/4384573-3 | |
| 650 | 7 | |a Nichtabelsche Gruppe |2 gnd |0 http://d-nb.info/gnd/4340007-3 | |
| 700 | 1 | |a Kim, Minhyong. | |
| 700 | 1 | |a Pop, Florian. | |
| 700 | 1 | |a Saïdi, Mohamed. | |
| 700 | 1 | |a Schneider, Peter. | |
| 776 | 0 | 8 | |i Print version: |z 9781107648852 |
| 830 | 0 | |a London Mathematical Society lecture note series. |0 http://id.loc.gov/authorities/names/n42015587 | |
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| 880 | 8 | |6 505-01/(S |a 5 Analogue of the MH(G) conjecture for Hida families -- 6 Vanishing of the R-torsion -- References -- Galois theory and Diophantine geometry -- 1 The deficiency of abelian motives -- 2 Motivic fundamental groups and Selmer varieties -- 3 Diophantine finiteness -- 4 An explicit formula and speculations -- References -- Potential modularity -- a survey -- 1 Introduction -- 2 Semistable elliptic curves over Q are modular -- 3 Why the semistability assumption-- 4 All elliptic curves over Q are modular -- 5 Kisin's modularity lifting theorems -- 6 Generalisations to totally real fields -- 7 Potential modularity pre-Kisin and the p-λ trick -- 8 Potential modularity after Kisin -- 9 Some final remarks -- References -- Remarks on some locally Qp-analyticrep resentations of GL2(F) in the crystalline case -- 1 Introduction and notations -- 2 Quick review of the GL2(Qp)-case -- 3 Quick review of weakly admissible filtered φ-modules -- 4 Some locally Qp-analytic representations of GL2(F) -- 5 Weak admissibility and GL2(F)-unitarity I -- 6 Amice-Vélu and Vishik revisited -- 7 Weak admissibility and GL2(F)-unitarity II -- 8 Local-global considerations -- 9 The case where the Galois representation is reducible -- References -- Completed cohomology -- a survey -- 1 Definitions -- 2 Non-commutative Iwasawa theory -- 3 Poincaré duality -- 4 A simple example of everything so far -- 5 Congruence quotients of symmetric spaces -- 6 Conjectures on codimensions -- 7 Mod p analogues -- 8 Heuristics related to the p-adic Langlands programme -- References -- Tensor and homotopy criteria for functional equations of ℓ-adic and classical iterated integrals -- 1 Introduction -- 2 Multi-Kummer characters -- 3 Multi-Kummer duals -- 4 Iterated integrals and their functional equations -- 5 Case of polylogarithms -- 6 Examples -- References. | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn775870071 |
|---|---|
| _version_ | 1813903427258810368 |
| adam_text | |
| any_adam_object | |
| author | Coates, John |
| author2 | Kim, Minhyong Pop, Florian Saïdi, Mohamed Schneider, Peter |
| author2_role | |
| author2_variant | m k mk f p fp m s ms p s ps |
| author_facet | Coates, John Kim, Minhyong Pop, Florian Saïdi, Mohamed Schneider, Peter |
| author_role | |
| author_sort | Coates, John |
| author_variant | j c jc |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 .N56 2011 |
| callnumber-search | QA247 .N56 2011 |
| callnumber-sort | QA 3247 N56 42011 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover; LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES; Title; Copyright; Contents; Contributors; Preface; Lectures on anabelian phenomena in geometry and arithmetic; Part I. Introduction and motivation; A. First examples; B. Galois characterization of global fields; Part II. Grothendieck's anabelian geometry; A. Warm-up: birational anabelian conjectures; B. Anabelian conjectures for curves; C. The section conjectures; Part III. Beyond the arithmetical action; A. Small Galois groups and valuations; B. Variation of fundamental groups in families of curves. |
| ctrlnum | (OCoLC)775870071 |
| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn775870071 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-25T16:18:30Z |
| institution | BVB |
| isbn | 9781139221580 1139221582 9786613580474 6613580473 9781139225014 1139225014 1139218492 9781139218498 9780511984440 0511984448 |
| language | English |
| oclc_num | 775870071 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (322 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series. |
| series2 | London Mathematical Society Lecture Note Series |
| spelling | Coates, John. Non-abelian Fundamental Groups and Iwasawa Theory. Cambridge : Cambridge University Press, 2011. 1 online resource (322 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society Lecture Note Series Print version record. Displays the intricate interplay between different foundations of non-commutative number theory. 880-01 Cover; LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES; Title; Copyright; Contents; Contributors; Preface; Lectures on anabelian phenomena in geometry and arithmetic; Part I. Introduction and motivation; A. First examples; B. Galois characterization of global fields; Part II. Grothendieck's anabelian geometry; A. Warm-up: birational anabelian conjectures; B. Anabelian conjectures for curves; C. The section conjectures; Part III. Beyond the arithmetical action; A. Small Galois groups and valuations; B. Variation of fundamental groups in families of curves. Includes bibliographical references. Iwasawa theory. http://id.loc.gov/authorities/subjects/sh2002004431 Non-Abelian groups. http://id.loc.gov/authorities/subjects/sh85092216 Iwasawa theory. Non-Abelian groups. Théorie d'Iwasawa. Groupes non abéliens. MATHEMATICS Number Theory. bisacsh Iwasawa theory fast Non-Abelian groups fast Aufsatzsammlung gnd Iwasawa-Theorie gnd http://d-nb.info/gnd/4384573-3 Nichtabelsche Gruppe gnd http://d-nb.info/gnd/4340007-3 Kim, Minhyong. Pop, Florian. Saïdi, Mohamed. Schneider, Peter. Print version: 9781107648852 London Mathematical Society lecture note series. 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=416715 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=416715 Volltext 505-01/(S 5 Analogue of the MH(G) conjecture for Hida families -- 6 Vanishing of the R-torsion -- References -- Galois theory and Diophantine geometry -- 1 The deficiency of abelian motives -- 2 Motivic fundamental groups and Selmer varieties -- 3 Diophantine finiteness -- 4 An explicit formula and speculations -- References -- Potential modularity -- a survey -- 1 Introduction -- 2 Semistable elliptic curves over Q are modular -- 3 Why the semistability assumption-- 4 All elliptic curves over Q are modular -- 5 Kisin's modularity lifting theorems -- 6 Generalisations to totally real fields -- 7 Potential modularity pre-Kisin and the p-λ trick -- 8 Potential modularity after Kisin -- 9 Some final remarks -- References -- Remarks on some locally Qp-analyticrep resentations of GL2(F) in the crystalline case -- 1 Introduction and notations -- 2 Quick review of the GL2(Qp)-case -- 3 Quick review of weakly admissible filtered φ-modules -- 4 Some locally Qp-analytic representations of GL2(F) -- 5 Weak admissibility and GL2(F)-unitarity I -- 6 Amice-Vélu and Vishik revisited -- 7 Weak admissibility and GL2(F)-unitarity II -- 8 Local-global considerations -- 9 The case where the Galois representation is reducible -- References -- Completed cohomology -- a survey -- 1 Definitions -- 2 Non-commutative Iwasawa theory -- 3 Poincaré duality -- 4 A simple example of everything so far -- 5 Congruence quotients of symmetric spaces -- 6 Conjectures on codimensions -- 7 Mod p analogues -- 8 Heuristics related to the p-adic Langlands programme -- References -- Tensor and homotopy criteria for functional equations of ℓ-adic and classical iterated integrals -- 1 Introduction -- 2 Multi-Kummer characters -- 3 Multi-Kummer duals -- 4 Iterated integrals and their functional equations -- 5 Case of polylogarithms -- 6 Examples -- References. |
| spellingShingle | Coates, John Non-abelian Fundamental Groups and Iwasawa Theory. London Mathematical Society lecture note series. Cover; LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES; Title; Copyright; Contents; Contributors; Preface; Lectures on anabelian phenomena in geometry and arithmetic; Part I. Introduction and motivation; A. First examples; B. Galois characterization of global fields; Part II. Grothendieck's anabelian geometry; A. Warm-up: birational anabelian conjectures; B. Anabelian conjectures for curves; C. The section conjectures; Part III. Beyond the arithmetical action; A. Small Galois groups and valuations; B. Variation of fundamental groups in families of curves. Iwasawa theory. http://id.loc.gov/authorities/subjects/sh2002004431 Non-Abelian groups. http://id.loc.gov/authorities/subjects/sh85092216 Iwasawa theory. Non-Abelian groups. Théorie d'Iwasawa. Groupes non abéliens. MATHEMATICS Number Theory. bisacsh Iwasawa theory fast Non-Abelian groups fast Aufsatzsammlung gnd Iwasawa-Theorie gnd http://d-nb.info/gnd/4384573-3 Nichtabelsche Gruppe gnd http://d-nb.info/gnd/4340007-3 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2002004431 http://id.loc.gov/authorities/subjects/sh85092216 http://d-nb.info/gnd/4384573-3 http://d-nb.info/gnd/4340007-3 |
| title | Non-abelian Fundamental Groups and Iwasawa Theory. |
| title_auth | Non-abelian Fundamental Groups and Iwasawa Theory. |
| title_exact_search | Non-abelian Fundamental Groups and Iwasawa Theory. |
| title_full | Non-abelian Fundamental Groups and Iwasawa Theory. |
| title_fullStr | Non-abelian Fundamental Groups and Iwasawa Theory. |
| title_full_unstemmed | Non-abelian Fundamental Groups and Iwasawa Theory. |
| title_short | Non-abelian Fundamental Groups and Iwasawa Theory. |
| title_sort | non abelian fundamental groups and iwasawa theory |
| topic | Iwasawa theory. http://id.loc.gov/authorities/subjects/sh2002004431 Non-Abelian groups. http://id.loc.gov/authorities/subjects/sh85092216 Iwasawa theory. Non-Abelian groups. Théorie d'Iwasawa. Groupes non abéliens. MATHEMATICS Number Theory. bisacsh Iwasawa theory fast Non-Abelian groups fast Aufsatzsammlung gnd Iwasawa-Theorie gnd http://d-nb.info/gnd/4384573-3 Nichtabelsche Gruppe gnd http://d-nb.info/gnd/4340007-3 |
| topic_facet | Iwasawa theory. Non-Abelian groups. Théorie d'Iwasawa. Groupes non abéliens. MATHEMATICS Number Theory. Iwasawa theory Non-Abelian groups Aufsatzsammlung Iwasawa-Theorie Nichtabelsche Gruppe |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=416715 |
| work_keys_str_mv | AT coatesjohn nonabelianfundamentalgroupsandiwasawatheory AT kimminhyong nonabelianfundamentalgroupsandiwasawatheory AT popflorian nonabelianfundamentalgroupsandiwasawatheory AT saidimohamed nonabelianfundamentalgroupsandiwasawatheory AT schneiderpeter nonabelianfundamentalgroupsandiwasawatheory |