Corpus ID: 237635017

Cohomology of semisimple local systems and the Decomposition theorem

@inproceedings{Wei2021CohomologyOS,
  title={Cohomology of semisimple local systems and the Decomposition theorem},
  author={Chuanhao Wei and Ruijie Yang},
  year={2021}
}
  • Chuanhao Wei, Ruijie Yang
  • Published 23 September 2021
  • Mathematics
In this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we establish a generalization of Hodge-Riemann bilinear relations. For a semisimple local system on a smooth projective variety, we define a canonical isomorphism from the complex conjugate of its cohomology to the cohomology of the dual local system, which is a generalization of the classical Weil operator for pure Hodge structures. This isomorphism establishes a… Expand

References

SHOWING 1-10 OF 38 REFERENCES
Absolute sets and the decomposition theorem
  • Nero Budur, B. Wang
  • Mathematics
  • Annales scientifiques de l'École normale supérieure
  • 2020
We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-HilbertExpand
Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization
The fundamental group is one of the most basic topological invariants of a space. The aim of this paper is to present a method of constructing representations of fundamental groups in complexExpand
The Hodge theory of algebraic maps
Abstract We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complexExpand
Hodge theory and complex algebraic geometry
Introduction. Part I. The Topology of Algebraic Varieties: 1. The Lefschetz theorem on hyperplane sections 2. Lefschetz pencils 3. Monodromy 4. The Leray spectral sequence Part II. Variations ofExpand
Mixed twistor structures
The purpose of this paper is to introduce the notion of mixed twistor structure, a generalization of the notion of mixed Hodge structure. The utility of this notion is to make possible a theory ofExpand
The decomposition theorem, perverse sheaves and the topology of algebraic maps
We give a motivated introduction to the theory of perverse sheaves, culminating in the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how theExpand
On a conjecture of Kashiwara
Kashiwara conjectured that the hard Lefshetz theorem and the semisimplicity theorem hold for any semisimple perverse sheaf M on a variety over a field of characteristic 0. He also conjectured that ifExpand
Polarizable twistor D-modules
We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety.Expand
D-Modules, Perverse Sheaves, and Representation Theory
D-Modules and Perverse Sheaves.- Preliminary Notions.- Coherent D-Modules.- Holonomic D-Modules.- Analytic D-Modules and the de Rham Functor.- Theory of Meromorphic Connections.- Regular HolonomicExpand
The perverse filtration and the Lefschetz Hyperplane Theorem
The perverse filtration in cohomology and in cohomology with compact supports is interpreted in terms of kernels of restrictions maps to suitable subvarieties by using the Lefschetz hyperplaneExpand
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