Hecke operators on topological modular forms

Autor:	Davies, Jack Morgan
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Topology Mathematics - Algebraic Geometry Mathematics - Number Theory 11F23 11F25 14D23 55N34 55N22 55P43 55S25
Zdroj:	Advances in Mathematics, Volume 452, 2024
Druh dokumentu:	Working Paper
Popis:	The cohomology theory TMF of topological modular forms is a derived algebro-geometric interpretation of the classical ring of complex modular forms from number theory. In this article, we refine the classical Adams operations, Hecke operators, and Atkin--Lehner involutions from endomorphisms of classical modular forms to stable operators on TMF. Our algebro-geometric formulation of these operators leads to simple proofs of their many remarkable properties and computations. From these properties, we use techniques from homotopy theory to make simple number-theoretic deductions, including a rederivation of some classical congruences of Ramanujan and providing new infinite families of classical Hecke operators which satisfy Maeda's conjecture. Comment: 60 pages, comments welcome, v2: updated version following referees suggestions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.06208 Zobrazit plný text záznamu View this record from Arxiv