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 |
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 | 1316991792 |
Understanding Galois representations is one of the central goals of number theory. Around 1990, Fontaine devised a strategy to compare such p-adic Galois representations to seemingly much simpler objects of (semi)linear algebra, the so-called etale (phi, gamma)-modules. This book is the first to provide a detailed and self-contained introduction to this theory. The close connection between the absolute Galois groups of local number fields and local function fields in positive characteristic is established using the recent theory of perfectoid fields and the tilting correspondence. The author works in the general framework of Lubin–Tate extensions of local number fields, and provides an introduction to Lubin–Tate formal groups and to the formalism of ramified Witt vectors. This book will allow graduate students to acquire the necessary basis for solving a research problem in this area, while also offering researchers many of the basic results in one convenient location.
Perfectoid Spaces
Title | Perfectoid Spaces PDF eBook |
Author | Debargha Banerjee |
Publisher | Springer Nature |
Pages | 395 |
Release | 2022-04-21 |
Genre | Mathematics |
ISBN | 9811671214 |
This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These contributions are presented at the conference on “Perfectoid Spaces” held at the International Centre for Theoretical Sciences, Bengaluru, India, from 9–20 September 2019. The objective of the book is to give an advanced introduction to Scholze’s theory and understand the relation between perfectoid spaces and some aspects of arithmetic of modular (or, more generally, automorphic) forms such as representations mod p, lifting of modular forms, completed cohomology, local Langlands program, and special values of L-functions. All chapters are contributed by experts in the area of arithmetic geometry that will facilitate future research in the direction.
Galois Module Structure
Title | Galois Module Structure PDF eBook |
Author | Victor Percy Snaith |
Publisher | American Mathematical Soc. |
Pages | 218 |
Release | 1994 |
Genre | Mathematics |
ISBN | 082180264X |
Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. This title addresses the Chinburg conjectures. It provides the background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions.
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.
Galois Groups and Fundamental Groups
Title | Galois Groups and Fundamental Groups PDF eBook |
Author | Tamás Szamuely |
Publisher | Cambridge University Press |
Pages | 281 |
Release | 2009-07-16 |
Genre | Mathematics |
ISBN | 0521888506 |
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Galois Groups and Their Representations
Title | Galois Groups and Their Representations PDF eBook |
Author | Yasutaka Ihara |
Publisher | Elsevier Science & Technology |
Pages | 190 |
Release | 1983 |
Genre | Mathematics |
ISBN |
This volume centres around the structure and the representations of the Galois groups of local or global fields including higher dimensional fields.