Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Galois Representations and (Phi, Gamma)-Modules
  • Cited by 10
Publisher:
Cambridge University Press
Online publication date:
May 2017
Print publication year:
2017
Online ISBN:
9781316981252
DOI:
https://doi.org/10.1017/9781316981252
Subjects:
Mathematics (general), Mathematics, Number Theory, Algebra
Series:
Cambridge Studies in Advanced Mathematics (164)
Information

Book description

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.

Reviews

'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 Source: Mathematical Reviews

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Accessibility standard: Unknown

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.