Galois Representations and (Phi, Gamma)-Modules
Title | Galois Representations and (Phi, Gamma)-Modules PDF eBook |
Author | Peter Schneider |
Publisher | Cambridge University Press |
Pages | 157 |
Release | 2017-04-20 |
Genre | Mathematics |
ISBN | 110718858X |
A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.
Représentations p-adiques de groupes p-adiques I
Title | Représentations p-adiques de groupes p-adiques I PDF eBook |
Author | Laurent Berger |
Publisher | |
Pages | 420 |
Release | 2008 |
Genre | Group theory |
ISBN | 9782856292563 |
Automorphic Forms and Galois Representations: Volume 1
Title | Automorphic Forms and Galois Representations: Volume 1 PDF eBook |
Author | Fred Diamond |
Publisher | Cambridge University Press |
Pages | 385 |
Release | 2014-10-16 |
Genre | Mathematics |
ISBN | 1316062333 |
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 one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.
Moduli Stacks of Étale (φ, Γ)-Modules and the Existence of Crystalline Lifts
Title | Moduli Stacks of Étale (φ, Γ)-Modules and the Existence of Crystalline Lifts PDF eBook |
Author | Matthew Emerton |
Publisher | Princeton University Press |
Pages | 312 |
Release | 2022-12-13 |
Genre | Mathematics |
ISBN | 069124135X |
"Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize étale ([phi], [Gamma])-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. Matthew Emerton and Toby Gee use these stacks to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. They explicitly describe the irreducible components of the underlying reduced substacks and discuss the relationship between the geometry of these stacks and the Breuil-Mézard conjecture. Along the way, they prove a number of foundational results in p-adic Hodge theory that may be of independent interest"--
Multivariable (φ,Γ)-modules and Representations of Products of Galois Groups
Title | Multivariable (φ,Γ)-modules and Representations of Products of Galois Groups PDF eBook |
Author | Gheorghe Pupazan |
Publisher | |
Pages | |
Release | 2021* |
Genre | |
ISBN |
Automorphic Forms and Galois Representations
Title | Automorphic Forms and Galois Representations PDF eBook |
Author | Fred Diamond |
Publisher | Cambridge University Press |
Pages | 387 |
Release | 2014-10-16 |
Genre | Mathematics |
ISBN | 1107693632 |
Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
Automorphic Forms and Galois Representations: Volume 2
Title | Automorphic Forms and Galois Representations: Volume 2 PDF eBook |
Author | Fred Diamond |
Publisher | Cambridge University Press |
Pages | 387 |
Release | 2014-10-16 |
Genre | Mathematics |
ISBN | 1316062341 |
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.