THE P-ADIC SIMPSON CORRESPONDENCE (AM-193) by Ahmed Abbes, Michel Gros, Takeshi Tsuji ( 9780691170299 )

Item Details

Title:

THE P-ADIC SIMPSON CORRESPONDENCE (AM-193)

By:

Ahmed Abbes, Michel Gros, Takeshi Tsuji

Format:

Paperback

List price:

£75.00

Our price:

£60.00

Discount:

20% off

You save:

£15.00

ISBN 10:

0691170290

ISBN 13:

9780691170299

Availability:

Usually dispatched within 1-3 weeks.

Delivery rates

Stock:

Currently 0 available

Publisher:

PRINCETON UNIVERSITY PRESS

Pub. date:

9 February, 2016

Series:

Annals of Mathematics Studies

Pages:

616

Synopsis:

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra-namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost etale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.

Publication:

Imprint:

Princeton University Press

Returns:

Returnable

Some other items by this author:

ELEMENTS DE GEOMETRIE RIGIDE (HB)

IN TUNE WITH THE MOON (PB)

IN TUNE WITH THE MOON 2010 (PB)

IN TUNE WITH THE MOON 2012 (PB)

IN TUNE WITH THE MOON 2013 (PB)

P-ADIC SIMPSON CORRESPONDENCE AND HODGE-TATE LOCAL SYSTEMS