Hecke operators as operations in elliptic cohomology
نویسندگان
چکیده
منابع مشابه
Hecke Operators on Cohomology
Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke operators are introduced includes the group cohomology of discrete subgroups of a semisimple Lie group, the de Rham c...
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Introduction. In our earlier papers [2,3,4,5,6], we investigated stable operations and cooperations in elliptic cohomology and its variants, relating these to known operations on rings of modular forms. The purpose of this article is to give an introduction to these stable operation algebras, in particular explaining the connections with Hecke algebras and Morava stabilizer algebras; further de...
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We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms.
متن کاملHecke Operations and the Adams E2-term Based on Elliptic Cohomology
The aim of this note is to rederive this result with the aid of stable operations related to the Hecke operators which were originally constructed in [1,2] and discussed further in [5,6]. Hitherto, these operations appear to have lacked serious topological applications. Our approach is modelled on one previously used in proving the analogous result in K-theory, Ext KU∗KU (KU∗,KU∗) ∼= Z/m(|n|) i...
متن کاملHecke Operators on the q-Analogue of Group Cohomology
We construct the q-analogue of a certain class of group cohomology and introduce the action of Hecke operators on such cohomology. We also show that such an action determines a representation of a Hecke ring in each of the associated group cohomology spaces. MSC 2000: 20G10, 11F60 (primary); 11F75, 18G99 (secondary)
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1990
ISSN: 0022-4049
DOI: 10.1016/0022-4049(90)90052-j