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Non-vanishing mod $p$ of derived Hecke algebra of the multiplicative group over number field

Dohyeong Kim, Jaesung Kwon

Abstract

We investigate the derived Hecke action on the cohomology of an arithmetic manifold associated to the multiplicative group over a number field. The degree one part of the action is proved to be non-vanishing modulo $p$ under mild assumptions. The main ingredient is the Grunwald--Wang theorem.

Non-vanishing mod $p$ of derived Hecke algebra of the multiplicative group over number field

Abstract

We investigate the derived Hecke action on the cohomology of an arithmetic manifold associated to the multiplicative group over a number field. The degree one part of the action is proved to be non-vanishing modulo under mild assumptions. The main ingredient is the Grunwald--Wang theorem.

Paper Structure

This paper contains 6 sections, 16 theorems, 50 equations.

Table of Contents

  1. Introduction
  2. Torus over number field
  3. Derived Hecke algebra of torus over number field
  4. Derived Hecke operator
  5. Derived Hecke algebra
  6. Non-vanishing mod p of derived Hecke algebra

Key Result

Proposition 2.1

The followings are true:

Theorems & Definitions (40)

  • Definition 1.1: Abstract derived Hecke algebra, Venkatesh venkatesh2016derived
  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Remark 2.4
  • Definition 3.1
  • Remark 3.2
  • ...and 30 more