Galois Representations and (Phi, Gamma)-Modules

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.

Author: Peter Schneider
Publisher: Cambridge University Press
Published: 04/20/2017
Pages: 156
Binding Type: Hardcover
Weight: 0.78lbs
Size: 9.37h x 6.33w x 0.57d
ISBN: 9781107188587

About the Author
Schneider, Peter: - 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.