Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Cohomology of Higgs isocrystals
View through CrossRef
This chapter describes the cohomology of Higgs isocrystals, which are introduced to replace the notion of Higgs bundles. The link between these two notions uses Higgs envelopes and calls to mind the link between classical crystals and modules with integrable connections. After discussing Higgs isocrystals and Higgs crystals, cohomology of Higgs isocrystals, and representations of the fundamental group, the chapter presents the main result: the construction of a fully faithful functor from the category of Higgs (iso)crystals satisfying an overconvergence condition to that of small generalized representations. It also proves the compatibility of this functor with the natural cohomologies and concludes by comparing the cohomology of Higgs isocrystals with Faltings cohomology.
Title: Cohomology of Higgs isocrystals
Description:
This chapter describes the cohomology of Higgs isocrystals, which are introduced to replace the notion of Higgs bundles.
The link between these two notions uses Higgs envelopes and calls to mind the link between classical crystals and modules with integrable connections.
After discussing Higgs isocrystals and Higgs crystals, cohomology of Higgs isocrystals, and representations of the fundamental group, the chapter presents the main result: the construction of a fully faithful functor from the category of Higgs (iso)crystals satisfying an overconvergence condition to that of small generalized representations.
It also proves the compatibility of this functor with the natural cohomologies and concludes by comparing the cohomology of Higgs isocrystals with Faltings cohomology.
Related Results
From Sheaf Cohomology to the Algebraic de Rham Theorem
From Sheaf Cohomology to the Algebraic de Rham Theorem
This chapter proves Grothendieck's algebraic de Rham theorem. It first proves Grothendieck's algebraic de Rham theorem more or less from scratch for a smooth complex projective var...
The Bloch–Kato Conjecture for the Riemann Zeta Function
The Bloch–Kato Conjecture for the Riemann Zeta Function
There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrati...
The Cohomology of Groups
The Cohomology of Groups
Abstract
This book presents an account of the theory of the cohomology ring of a finite group. The aim is to present a modern approach from the point of view of homo...
Almost étale coverings
Almost étale coverings
This chapter explains Faltings' theory of almost étale extensions, a tool that has become essential in many questions in arithmetic geometry, even beyond p-adic Hodge theory. It be...
The Hodge Theory of Maps
The Hodge Theory of Maps
This chapter showcases two further lectures on the Hodge theory of maps, and they are mostly composed of exercises. The first lecture details a minimalist approach to sheaf cohomol...
The Linear Spencer Sequence
The Linear Spencer Sequence
The three-term nonlinear Spencer sequence constructed in Chapter 8 extends to a linear sequence. This construction explains the “deformation cohomology” of Chapter 9 and raises som...
Period Domains and Period Mappings
Period Domains and Period Mappings
This chapter seeks to develop a working understanding of the notions of period domain and period mapping, as well as familiarity with basic examples thereof. It first reviews the n...
Facets of Algebraic Geometry
Facets of Algebraic Geometry
Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and relate...