The p adic Simpson Correspondence AM 193 is popular PDF and ePub book, written by Ahmed Abbes in 2016-02-09, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The p adic Simpson Correspondence AM 193 can be Read Online from any device for your convenience.
The p adic Simpson Correspondence AM 193 Book PDF Summary
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 étale 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.
Detail Book of The p adic Simpson Correspondence AM 193 PDF
- Author : Ahmed Abbes
- Release : 09 February 2016
- Publisher : Princeton University Press
- ISBN : 9780691170299
- Genre : Mathematics
- Total Page : 617 pages
- Language : English
- PDF File Size : 7,8 Mb
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