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 ...
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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 ???tale 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.
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Add this copy of The P-Adic Simpson Correspondence (Am-193) (Annals of to cart. $86.00, like new condition, Sold by Academybookshop rated 3.0 out of 5 stars, ships from Long Island City, NY, UNITED STATES, published 2016 by Princeton University Press.
Add this copy of The P-Adic Simpson Correspondence to cart. $149.57, like new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2016 by Princeton University Press.
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Fine. Sewn binding. Cloth over boards. 616 p. Annals of Mathematics Studies, 193. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
