Holomorphic de Rham Complexes and Spectral Sequences

2002 ◽  
pp. 184-216
Keyword(s):  
Spectral Sequences ◽  
De Rham

scholarly journals Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

scholarly journals THE VAN EST SPECTRAL SEQUENCE FOR HOPF ALGEBRAS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 33-48 ◽  
Author(s):  
E. J. BEGGS ◽  
TOMASZ BRZEZIŃSKI
Keyword(s):  
Hopf Algebra ◽  
Spectral Sequence ◽  
Lie Algebra ◽  
Hopf Algebras ◽  
Cohomology Group ◽  
Spectral Sequences ◽  
De Rham Cohomology ◽  
Lie Algebra Cohomology ◽  
De Rham ◽  
Definition Of

Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduced. A definition of Hopf–Lie algebra cohomology is also given.

Mixed Hodge Structures

2017 ◽  
Author(s):  
Fouad El Zein ◽  
Lˆe D˜ung Tr ´ang
Keyword(s):  
Spectral Sequence ◽  
Linear Algebra ◽  
Algebraic Variety ◽  
Spectral Sequences ◽  
Hodge Structures ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham ◽  
Definition Of ◽  
Mixed Hodge Structures

This chapter discusses mixed Hodge structures (MHS). It first defines the abstract category of Hodge structures and introduces spectral sequences. The decomposition on the cohomology of Kähler manifolds is used to prove the degeneration at rank 1 of the spectral sequence defined by the filtration F on the de Rham complex in the projective nonsingular case. The chapter then introduces an abstract definition of MHS as an object of interest in linear algebra. It then attempts to develop algebraic homology techniques on filtered complexes up to filtered quasi-isomorphisms of complexes. Finally, this chapter provides the construction of the MHS on any algebraic variety.

THE DE RHAM COHOMOLOGY OF DIFFERENTIAL SPACES

1989 ◽  
Vol 22 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Wiesław Sasin
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Differential Spaces

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals A de Rham model for complex analytic equivariant elliptic cohomology

2021 ◽  
Vol 380 ◽  
pp. 107575
Author(s):  
Daniel Berwick-Evans ◽  
Arnav Tripathy
Keyword(s):  
Elliptic Cohomology ◽  
De Rham
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