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El. knyga: Automorphic Forms and Galois Representations: Volume 2

Edited by (University of Oxford), Edited by (King's College London), Edited by (King's College London)
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Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.

This collection, the second of two volumes arising from an LMS-EPSRC Durham Symposium, explores the importance of automorphic forms and Galois representations in number theory. The expository articles and research papers within cover recent progress in anabelian geometry, p-adic Hodge theory, the Langlands program, and p-adic methods in number theory.

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Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
List of contributors
vi
Preface vii
1 On the local structure of ordinary Hecke algebras at classical weight one points
1(16)
Mladen Dimitrov
2 Vector bundles on curves and p-adic Hodge theory
17(88)
Laurent Fargues
Jean-Marc Fontaine
3 Around associators
105(13)
Hidekazu Furusho
4 The stable Bernstein center and test functions for Shimura varieties
118(69)
Thomas J. Haines
5 Conditional results on the birational section conjecture over small number fields
187(44)
Yuichiro Hoshi
6 Blocks for mod p representations of GL2(Qp)
231(17)
Vytautas Paskunas
7 From etale P+-representations to G-equivariant sheaves on G/P
248(119)
Peter Schneider
Marie-France Vigneras
Gergely Zabradi
8 Intertwining of ramified and unramified zeros of Iwasawa modules
367
Chandrashekhar Khare
Jean-Pierre Wintenberger
Minhyong Kim is a Professor of Number Theory at the University of Oxford. Fred Diamond is a Professor of Mathematics at King's College London. Payman Kassaei is an Associate Professor of Mathematics at McGill University.