p-adic Simpson Correspondence (eBook)

Ahmed Abbes, Michel Gros, Takeshi Tsuji (Autoren)

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2016
616 Seiten
Princeton University Press (Verlag)
978-1-4008-8123-9 (ISBN)

Infos

Ahmed Abbes is director of research at the French National Center for Scientific Research (CNRS) and the Institute of Advanced Scientific Studies (IHÉS), 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.

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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.

Produkt-Details

• Erscheint lt. Verlag: 9.2.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Abelian category • Addition • additive categories • Additive category • adic module • Adjoint • Adjoint functors • Adjunction (field theory) • affine transformation • algebraic closure • almost faithfully flat descent • almost faithfully flat module • almost flat module • almost isomorphism • almost tale covering • almost tale extension • automorphism • Base change • bijection • Canonical map • Category of sets • Closed immersion • Codimension • coefficient • cohomology • Cokernel • Commutative diagram • commutative property • Commutative Ring • Compact space • Computation • Connected component (graph theory) • Connected space • corollary • covanishing topos • Covering space • crystalline-type topos • Cup product • Deformation • derived category • Diagram (category theory) • Direct image functor • Direct limit • direct sum • discrete AЇ-module • Discrete valuation ring • Divisibility rule • Divisor • Dolbeault generalized representation • Dolbeault module • Dolbeault representation • Embedding • Endomorphism • Equivalence of Categories • Exact functor • exactness • exact sequence • existential quantification • exponential function • Faltings cohomology • Faltings extension • Faltings ringed topos • Faltings site • Faltings topos • Fibred category • Field of fractions • finite tale site • Formal scheme • functor • fundamental group • galois cohomology • Galois group • generalized covanishing topos • generalized representation • Generic point • Gerd Faltings • Groupoid • Higgs bundle • Higgs bundles • Higgs crystals • Higgs envelopes • Higgs isocrystal • HiggsДate algebra • Hodge Theory • HodgeДate representation • HodgeДate structure • HodgeДate theory • Homomorphism • Hyodo's theory • Identity element • Initial and terminal objects • Injective object • Integer • integral domain • Integral element • Inverse image functor • Inverse limit • Inverse System • Irreducible component • Koszul complex • linear algebra • locally irreducible scheme • logarithm • Mathematical Induction • Maximal Ideal • Module (mathematics) • Monoid • Morphism • Morphism of schemes • overconvergence • p-adic field • p-adic Hodge theory • P-adic number • p-adic Simpson correspondence • period ring • Presheaf (category theory) • Principal homogeneous space • Profinite group • pullback • Rational number • Representation Theory • residue field • Right inverse • ringed covanishing topos • ringed total topos • ring homomorphism • scientific notation • Sheaf (mathematics) • small generalized representation • small representation • Smooth morphism • solvable Higgs module • Spectral Sequence • subcategory • SUBGROUP • Summation • symmetric algebra • tale cohomology • tale fundamental group • tensor product • Theorem • Topological ring • Topology • torsor • Torsor (algebraic geometry) • Trivial representation • Valuation ring • vector bundle • Zariski topology
• ISBN-10: 1-4008-8123-4 / 1400881234
• ISBN-13: 978-1-4008-8123-9 / 9781400881239