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.

scholarly journals Bordered Floer homology and the spectral sequence of a branched double cover II: the spectral sequences agree

2016 ◽  
Vol 9 (2) ◽  
pp. 607-686
Author(s):  
Robert Lipshitz ◽  
Peter S. Ozsváth ◽  
Dylan P. Thurston
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Double Cover ◽  
Spectral Sequences

Motivic cohomology of quadrics and the coniveau spectral sequence

2010 ◽  
Vol 6 (3) ◽  
pp. 547-589 ◽  
Author(s):  
Nobuaki Yagita
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Motivic Cohomology

AbstractWe study the coniveau spectral sequence for quadrics defined by Pfister forms. In particular, we explicitly compute the motivic cohomology of anisotropic quadrics over ℝ, by showing that their coniveau spectral sequences collapse from the -term

Spectral Sequences

2020 ◽  
pp. 45-56
Author(s):  
Loring W. Tu
Keyword(s):  
Projective Plane ◽  
Spectral Sequence ◽  
Fiber Bundles ◽  
Spectral Sequences ◽  
Complex Projective Plane ◽  
Computational Tool ◽  
Short Introduction ◽  
Complex Projective

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined by Jean-Louis Koszul, Henri Cartan, Jean-Pierre Serre, and many others. The chapter provides a short introduction, without proofs, to spectral sequences. As an example, it computes the cohomology of the complex projective plane. The chapter then details Leray's theorem. A spectral sequence is like a book with many pages. Each time one turns a page, one obtains a new page that is the cohomology of the previous page.

scholarly journals A generalization of Kita and Noumi’s vanishing theorems of cohomology groups of local system

1997 ◽  
Vol 147 ◽  
pp. 63-69 ◽  
Author(s):  
Koji Cho
Keyword(s):  
Algebraic Geometry ◽  
Spectral Sequence ◽  
Local System ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Cohomology Groups ◽  
De Rham

AbstractWe prove vanishing theorems of cohomology groups of local system, which generalize Kita and Noumi’s result and partially Aomoto’s result. Main ingredients of our proof are the Hodge to de Rham spectral sequence and Serre’s vanishing theorem in algebraic geometry.

scholarly journals Model category structures and spectral sequences

2019 ◽  
Vol 150 (6) ◽  
pp. 2815-2848
Author(s):  
Joana Cirici ◽  
Daniela Egas Santander ◽  
Muriel Livernet ◽  
Sarah Whitehouse
Keyword(s):  
Spectral Sequence ◽  
Commutative Ring ◽  
Model Category ◽  
Spectral Sequences ◽  
Model Structures

AbstractLet R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and décalage.

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