scholarly journals A basis of algebraic de Rham cohomology of complete intersections over a characteristic zero field

2021 ◽  
pp. 1-17
Author(s):  
Jeehoon Park ◽  
Junyeong Park
Keyword(s):  
Characteristic Zero ◽  
Complete Intersections ◽  
Zero Field ◽  
De Rham Cohomology ◽  
De Rham ◽  
Algebraic De Rham Cohomology

scholarly journals The Algebraic de Rham Cohomology of Representation Varieties

2018 ◽  
Vol 70 (3) ◽  
pp. 702-720
Author(s):  
Eugene Z. Xia
Keyword(s):  
De Rham Cohomology ◽  
Natural Family ◽  
De Rham ◽  
The One ◽  
Representation Varieties ◽  
Algebraic De Rham Cohomology ◽  
Natural Families

AbstractThe SL(2, ℂ)-representation varieties of punctured surfaces form natural families parameterized by monodromies at the punctures. In this paper, we compute the loci where these varieties are singular for the cases of one-holed and two-holed tori and the four-holed sphere. We then compute the de Rham cohomologies of these varieties of the one-holed torus and the four-holed sphere when the varieties are smooth via the Grothendieck theorem. Furthermore, we produce the explicit Gauß-Manin connection on the natural family of the smooth SL(2, ℂ)-representation varieties of the one-holed torus.

scholarly journals de Rham cohomology of local cohomology modules: The graded case

2015 ◽  
Vol 217 ◽  
pp. 1-21
Author(s):  
Tony J. Puthenpurakal
Keyword(s):  
Characteristic Zero ◽  
Weyl Algebra ◽  
Local Cohomology ◽  
Isolated Singularity ◽  
De Rham Cohomology ◽  
Local Cohomology Modules ◽  
De Rham ◽  
Positive Integers ◽  
Cohomology Modules ◽  
Koszul Cohomology

AbstractLetKbe a field of characteristic zero, and letR = K[X1,… ,Xn]. Let An(K) = K⟨X1,… ,Xn,∂1,… ,∂n⟩ be thenth Weyl algebra overK. We consider the case whenRandAn(K) are graded by giving degXi= ωiand deg∂i=–ωifori= 1,…,n(hereωiare positive integers). Set. LetIbe a graded ideal inR. By a result due to Lyubeznik the local cohomology modulesare holonomic (An(K))-modules for eachi≥0. In this article we prove that the de Rham cohomology modulesare concentrated in degree —ω; that is,forj ≠ –ω. As an application whenA = R/(f) is an isolated singularity, we relatetoHn-1(∂(f);A), the (n –1)th Koszul cohomology ofAwith respect to∂1(f),…,∂n(f).

scholarly journals de Rham cohomology of local cohomology modules: The graded case

2015 ◽  
Vol 217 ◽  
pp. 1-21 ◽  
Author(s):  
Tony J. Puthenpurakal
Keyword(s):  
Characteristic Zero ◽  
Weyl Algebra ◽  
Local Cohomology ◽  
Isolated Singularity ◽  
De Rham Cohomology ◽  
Local Cohomology Modules ◽  
De Rham ◽  
Positive Integers ◽  
Cohomology Modules ◽  
Koszul Cohomology

AbstractLet K be a field of characteristic zero, and let R = K[X1,… ,Xn]. Let An(K) = K⟨X1,… ,Xn,∂1,… ,∂n⟩ be the nth Weyl algebra over K. We consider the case when R and An(K) are graded by giving deg Xi = ωi and deg ∂i = –ωi for i = 1,…,n (here ωi are positive integers). Set . Let I be a graded ideal in R. By a result due to Lyubeznik the local cohomology modules are holonomic (An(K))-modules for each i≥0. In this article we prove that the de Rham cohomology modules are concentrated in degree —ω; that is, for j ≠ –ω. As an application when A = R/(f) is an isolated singularity, we relate to Hn-1(∂(f);A), the (n – 1)th Koszul cohomology of A with respect to ∂1(f),…, ∂n(f).

Algebraic de Rham Cohomology

2017 ◽  
pp. 73-96
Author(s):  
Annette Huber ◽  
Stefan Müller-Stach
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Algebraic De Rham Cohomology

Algebraic De Rham cohomology

1972 ◽  
Vol 7 (2) ◽  
pp. 125-140 ◽  
Author(s):  
Robin Hartshorne
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Algebraic De Rham Cohomology

Poincar� duality for algebraic de rham cohomology

2004 ◽  
Vol 114 (1) ◽  
pp. 61-116 ◽  
Author(s):  
Luisa Fiorot ◽  
Maurizio Cailotto ◽  
Francesco Baldassarri
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Algebraic De Rham Cohomology

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 STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

2021 ◽  
pp. 1-48
Author(s):  
Federico Scavia
Keyword(s):  
Finite Groups ◽  
Reductive Groups ◽  
Orthogonal Groups ◽  
De Rham Cohomology ◽  
Algebraic Stacks ◽  
Steenrod Operations ◽  
De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

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