p-adic Simpson Correspondence
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€90.99
A01=Ahmed Abbes
A01=Michel Gros
A01=Takeshi Tsuji
Adjoint functors
Affine transformation
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Age Group_Uncategorized
Algebraic closure
Author_Ahmed Abbes
Author_Michel Gros
Author_Takeshi Tsuji
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Automorphism
Base change
Category1=Non-Fiction
Category=PBF
Closed immersion
Coefficient
Cohomology
Cokernel
Commutative diagram
Commutative property
Commutative ring
Computation
Connected component (graph theory)
COP=United States
Corollary
Covering space
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Derived category
Diagram (category theory)
Direct limit
Direct sum
Discrete valuation ring
Divisibility rule
Embedding
Endomorphism
eq_isMigrated=2
eq_nobargain
Equivalence of categories
Exact functor
Exact sequence
Existential quantification
Field of fractions
Formal scheme
Functor
Fundamental group
Galois cohomology
Galois group
Generic point
Higgs bundle
Hodge theory
Homomorphism
Identity element
Initial and terminal objects
Integer
Integral domain
Integral element
Inverse image functor
Inverse limit
Inverse system
Irreducible component
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Logarithm
Mathematical induction
Maximal ideal
Monoid
Morphism
Morphism of schemes
P-adic number
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Presheaf (category theory)
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Profinite group
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Rational number
Residue field
Ring homomorphism
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Spectral sequence
Subgroup
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Tensor product
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Topology
Torsor (algebraic geometry)
Valuation ring
Vector bundle
Zariski topology
Product details
- ISBN 9780691170299
- Weight: 1077g
- Dimensions: 178 x 254mm
- Publication Date: 09 Feb 2016
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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 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.
Ahmed Abbes is director of research at the French National Center for Scientific Research (CNRS) and the Institute of Advanced Scientific Studies (IHES), France. Michel Gros is a researcher at the CNRS. Takeshi Tsuji is a professor in the Graduate School of Mathematical Sciences at the University of Tokyo.
