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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The de Rham cohomology in characteristic 0
特征0 德拉姆 上同调
2023/4/19
Discuss [Bha, §2.3-2.4]. See [Dri20, §1.3] for the notion of cones and quasi-ideals. Note that some of the remarks (e.g. Remark 2.2.15) [Bha, §2.2] may not have been covered in Lecture 1. Explain them...
Eichler Cohomology of Generalized Modular Forms of Real Weights
Eichler Cohomology Generalized Modular Forms Number Theory
2012/5/9
In this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the...
On the Dimension of Cohomology of Bianchi Groups
Dimension Cohomology Bianchi Groups Number Theory
2012/4/18
Using Lefschetz numbers of certain involutions, we provide lower bounds for the cuspidal cohomology of principal congruence subgroups of Bianchi groups. The asymptotic lower bounds that follow from ou...
Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence
Shimura curves p-adic Jacquet-Langlands correspondence Number Theory
2011/8/25
Abstract: We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. ...
Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees
bigrading the combinatorial Hopf algebra rooted trees
2010/11/2
The renormalization of quantum field theory twists the antipode of a noncocommutative Hopf algebra of rooted trees, decorated by an infinite set of primitive divergences. The Hopf algebra of undecorat...