Galois Representations and

Phi, Gamma -Modules

Peter Schneider (Westfälische Wilhelms-Universität Münster, Germany)

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English

Cambridge University Press
20 April 2017

Number theory

Series: Cambridge Studies in Advanced Mathematics

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.

By: Peter Schneider (Westfälische Wilhelms-Universität Münster Germany)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 164
Dimensions: Height: 235mm, Width: 158mm, Spine: 14mm
Weight: 360g
ISBN: 9781107188587
ISBN 10: 110718858X
Series: Cambridge Studies in Advanced Mathematics
Pages: 156
Publication Date: 20 April 2017
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Peter Schneider is a professor in the Mathematical Institute at the University of Münster. His research interests lie within the Langlands program, which relates Galois representations to representations of p-adic reductive groups, as well as in number theory and in representation theory. He is the author of Nonarchimedean Functional Analysis (2001), p-Adic Lie Groups (2011) and Modular Representation Theory of Finite Groups (2012), and he is a member of the National German Academy of Science Leopoldina and of the Academia Europaea.

Reviews for Galois Representations and (Phi, Gamma)-Modules

'Much of this material is available in the literature, but it has never been presented so cleanly and concisely in a single place before … In this book, Schneider has done a remarkable job of displaying the beauty and power of perfectoid theoretic techniques. His text is sure to occupy and satisfy the attention of students and researchers working on Galois representations, or those who suspect that perfectoid-style techniques might be relevant for their work. We recommend Schneider's text to anyone with even a passing interest in the perfectoid revolution initiated by Scholze.' Cameron Franc, Mathematical Reviews