arXiv Analytics

Sign in

arXiv:2104.13407 [math.AT]AbstractReferencesReviewsResources

Constructing and calculating Adams operations on topological modular forms

Jack Morgan Davies

Published 2021-04-27Version 1

We construct stable Adams operations on the cohomology theory Tmf of topological modular forms. This is done by extending the sheaf defining Tmf to be functorial with respect to isogenies of generalised elliptic curves of invertible degree. These Adams operations are then calculated on the homotopy groups of Tmf using a combination of descent spectral sequences, the theory of synthetic spectra, and Anderson duality.

Comments: 43 pages, comments always welcome
Categories: math.AT, math.AG
Subjects: 55N34, 55N22, 55S25, 55P43, 11F23, 14F20
Related articles: Most relevant | Search more
arXiv:1312.7394 [math.AT] (Published 2013-12-28, updated 2015-02-03)
Topological modular forms with level structure
arXiv:2212.06208 [math.AT] (Published 2022-12-12)
Hecke operators on topological modular forms
arXiv:0910.5130 [math.AT] (Published 2009-10-27)
Topological modular forms (aftern Hopkins, Miller, and Lurie)

Links

Toolbox