Hecke Operations and the Adams E2-Term Based on Elliptic Cohomology
نویسندگان
چکیده
منابع مشابه
Hecke 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...
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We investigate the E2-term of Adams spectral sequence based on elliptic homology. The main results describe this E2-term from a ‘chromatic’ perspective. At a prime p > 3, the Bousfield class of Ell is the same as that of K(0)∨K(1)∨ K(2). Using delicate facts due to Katz (which also play a major rôle in work on the structure Ell∗Ell by Clarke & Johnson, the author and Laures) as well as our desc...
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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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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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The first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve. The second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups. The third part investigates the representation theoretic considerations which give rise to the power operations discussed in the first part.
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 1999
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-1999-015-2