scholarly journals A REMARK ON THE BRYLINSKI CONJECTURE FOR ORBIFOLDS

2011 ◽  
Vol 91 (1) ◽  
pp. 1-12 ◽  
Author(s):  
L. BAK ◽  
A. CZARNECKI
Keyword(s):  
Riemannian Foliation ◽  
De Rham Cohomology ◽  
De Rham ◽  
Leaf Space ◽  
Foliated Manifolds

AbstractThe paper presents a proof of the Brylinski conjecture for compact Kähler orbifolds. The result is a corollary of the foliated version of the Mathieu theorem on symplectic harmonic representations of de Rham cohomology classes. The proofs are based on the idea of representing an orbifold as the leaf space of a Riemannian foliation and on the correspondence between foliated and holonomy invariant objects for foliated manifolds.

scholarly journals On the de rham cohomology of the leaf space of a foliation

Topology ◽  
1974 ◽  
Vol 13 (2) ◽  
pp. 185-187 ◽  
Author(s):  
Gerald W. Schwarz
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Leaf Space

scholarly journals Twistor spaces on foliated manifolds

2021 ◽  
pp. 2150056
Author(s):  
Rouzbeh Mohseni ◽  
Robert A. Wolak
Keyword(s):  
Normal Bundle ◽  
Twistor Space ◽  
Riemannian Foliation ◽  
Holomorphic Mappings ◽  
Twistor Theory ◽  
Simple Consequence ◽  
Twistor Spaces ◽  
Leaf Space ◽  
Foliated Manifolds ◽  
Theory Lead

The theory of twistors on foliated manifolds is developed. We construct the twistor space of the normal bundle of a foliation. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic mappings. Since any orbifold can be understood as the leaf space of a suitably defined Riemannian foliation we obtain orbifold versions of the classical results as a simple consequence of the results on foliated mappings.

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 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 $p=2$ .

scholarly journals Cycles in the de Rham cohomology of abelian varieties over number fields

2018 ◽  
Vol 154 (4) ◽  
pp. 850-882
Author(s):  
Yunqing Tang
Keyword(s):  
Endomorphism Ring ◽  
Abelian Varieties ◽  
Number Fields ◽  
De Rham Cohomology ◽  
Tate Conjecture ◽  
De Rham ◽  
Prime Dimension

In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of$\ell$-adic Tate cycles. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius. Ogus predicted that such cycles coincide with Hodge cycles for abelian varieties. In this paper, we confirm Ogus’ prediction for some families of abelian varieties. These families include geometrically simple abelian varieties of prime dimension that have non-trivial endomorphism ring. The proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture.

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