O-minimality and diophantine geometry:
This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits,...
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| Other Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | London Mathematical Society lecture note series
421 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xii, 221 pages) |
| ISBN: | 9781316106839 |
| DOI: | 10.1017/CBO9781316106839 |
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| 505 | 8 | 0 | |t The Manin-Mumford Conjecture, an elliptic Curve, its Torsion Points & their Galois Orbits |r P. Habegger |t Rational points on definable sets |r A.J. Wilkie |t Functional transcendence via o-minimality |r Jonathan Pila |t Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem |r Martin Orr |t The André-Oort conjecture via o-minimality |r Christopher Daw |t Lectures on elimination theory for semialgebraic and subanalytic sets |r A.J. Wilkie |t Relative Manin-Mumford for abelian varieties |r D. Masser |t Improving the bound in the Pila-Wilkie theorem for curves |r G.O. Jones |t Ax-Schanuel and o-minimality |r Jacob Tsimerman |
| 520 | |a This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture | ||
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Record in the Search Index
| _version_ | 1804176880714121216 |
|---|---|
| any_adam_object | |
| author2 | Jones, G. O. Wilkie, A. J. |
| author2_role | edt edt |
| author2_variant | g o j go goj a j w aj ajw |
| author_additional | P. Habegger A.J. Wilkie Jonathan Pila Martin Orr Christopher Daw D. Masser G.O. Jones Jacob Tsimerman |
| author_facet | Jones, G. O. Wilkie, A. J. |
| building | Verbundindex |
| bvnumber | BV043940322 |
| classification_rvk | SK 240 |
| collection | ZDB-20-CBO |
| contents | The Manin-Mumford Conjecture, an elliptic Curve, its Torsion Points & their Galois Orbits Rational points on definable sets Functional transcendence via o-minimality Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem The André-Oort conjecture via o-minimality Lectures on elimination theory for semialgebraic and subanalytic sets Relative Manin-Mumford for abelian varieties Improving the bound in the Pila-Wilkie theorem for curves Ax-Schanuel and o-minimality |
| ctrlnum | (ZDB-20-CBO)CR9781316106839 (OCoLC)930540753 (DE-599)BVBBV043940322 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781316106839 |
| format | Electronic eBook |
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| spelling | O-minimality and diophantine geometry edited by G.O. Jones, University of Manchester, A.J. Wilkie, University of Manchester, O-Minimality & Diophantine Geometry Cambridge Cambridge University Press 2015 1 online resource (xii, 221 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 421 Title from publisher's bibliographic system (viewed on 05 Oct 2015) The Manin-Mumford Conjecture, an elliptic Curve, its Torsion Points & their Galois Orbits P. Habegger Rational points on definable sets A.J. Wilkie Functional transcendence via o-minimality Jonathan Pila Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem Martin Orr The André-Oort conjecture via o-minimality Christopher Daw Lectures on elimination theory for semialgebraic and subanalytic sets A.J. Wilkie Relative Manin-Mumford for abelian varieties D. Masser Improving the bound in the Pila-Wilkie theorem for curves G.O. Jones Ax-Schanuel and o-minimality Jacob Tsimerman This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture Arithmetical algebraic geometry Model theory Geometry, Analytic Diophantische Geometrie (DE-588)4150021-0 gnd rswk-swf O-Minimalität (DE-588)7544778-2 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content O-Minimalität (DE-588)7544778-2 s Diophantische Geometrie (DE-588)4150021-0 s 2\p DE-604 Jones, G. O. edt Wilkie, A. J. edt Erscheint auch als Druckausgabe 978-1-107-46249-6 https://doi.org/10.1017/CBO9781316106839 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | O-minimality and diophantine geometry The Manin-Mumford Conjecture, an elliptic Curve, its Torsion Points & their Galois Orbits Rational points on definable sets Functional transcendence via o-minimality Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem The André-Oort conjecture via o-minimality Lectures on elimination theory for semialgebraic and subanalytic sets Relative Manin-Mumford for abelian varieties Improving the bound in the Pila-Wilkie theorem for curves Ax-Schanuel and o-minimality Arithmetical algebraic geometry Model theory Geometry, Analytic Diophantische Geometrie (DE-588)4150021-0 gnd O-Minimalität (DE-588)7544778-2 gnd |
| subject_GND | (DE-588)4150021-0 (DE-588)7544778-2 (DE-588)4143413-4 |
| title | O-minimality and diophantine geometry |
| title_alt | O-Minimality & Diophantine Geometry The Manin-Mumford Conjecture, an elliptic Curve, its Torsion Points & their Galois Orbits Rational points on definable sets Functional transcendence via o-minimality Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem The André-Oort conjecture via o-minimality Lectures on elimination theory for semialgebraic and subanalytic sets Relative Manin-Mumford for abelian varieties Improving the bound in the Pila-Wilkie theorem for curves Ax-Schanuel and o-minimality |
| title_auth | O-minimality and diophantine geometry |
| title_exact_search | O-minimality and diophantine geometry |
| title_full | O-minimality and diophantine geometry edited by G.O. Jones, University of Manchester, A.J. Wilkie, University of Manchester, |
| title_fullStr | O-minimality and diophantine geometry edited by G.O. Jones, University of Manchester, A.J. Wilkie, University of Manchester, |
| title_full_unstemmed | O-minimality and diophantine geometry edited by G.O. Jones, University of Manchester, A.J. Wilkie, University of Manchester, |
| title_short | O-minimality and diophantine geometry |
| title_sort | o minimality and diophantine geometry |
| topic | Arithmetical algebraic geometry Model theory Geometry, Analytic Diophantische Geometrie (DE-588)4150021-0 gnd O-Minimalität (DE-588)7544778-2 gnd |
| topic_facet | Arithmetical algebraic geometry Model theory Geometry, Analytic Diophantische Geometrie O-Minimalität Aufsatzsammlung |
| url | https://doi.org/10.1017/CBO9781316106839 |
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