论文标题
Hecke操作员以拓扑模块化形式
Hecke operators on topological modular forms
论文作者
论文摘要
拓扑模块形式的同时理论TMF是对数字理论的复杂模块化形式的经典环的衍生代数几何解释。在本文中，我们完善了经典的Adams操作，Hecke运营商和Atkin - Lehner的参与，从经典模块化形式的内态性到TMF上稳定的操作员。我们对这些运算符的代数几何表述，可以简单地证明其许多显着的属性和计算。从这些属性中，我们使用同义理论中的技术来进行简单的数字理论推论，包括重新启动Ramanujan的某些经典一致性，并为满足Maeda猜想的经典Hecke操作员提供新的无限家族。
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.
