Galois Representations and (Phi, Gamma)-Modules
2017
First Published
198
Number of Pages
Part of Series
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
Author · 10 books
Peter Schneider is a German novelist. His novel Lenz, published in 1973, had become a cult text for the Left, capturing the feelings of those disappointed by the failure of their utopian revolt. Since then, Peter Schneider has written novels, short stories and film scripts, that often deal with the fate of members of his generation. Other works deal with the situation of Berlin before and after German reunification. Schneider is also a major Essayist; having moved away from the radicalism of 1968, his work now appears predominantly in bourgeois publications.
