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De Rham cohomology of Lubin-Tate spaces and Drinfeld spaces

Benchao Su

Abstract

Let $d\ge 1$ be an integer. We use the methods introduced by Lue Pan to prove that the compactly supported cohomology of Lubin-Tate towers and Drinfeld towers are isomorphic, as $\text{GL}_{d+1}(L)\times D_{L,\frac{1}{d+1}}^\times$-modules.

De Rham cohomology of Lubin-Tate spaces and Drinfeld spaces

Abstract

Let be an integer. We use the methods introduced by Lue Pan to prove that the compactly supported cohomology of Lubin-Tate towers and Drinfeld towers are isomorphic, as -modules.

Paper Structure

This paper contains 4 sections, 20 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. The flag variety
  3. The Lubin-Tate space at infinite level
  4. The Drinfeld space at infinite level

Key Result

Theorem 1.1

For any $i\ge 0$, there exists a $C$-linear $G\times \check G$-equivariant isomorphism of the compactly supported de Rham cohomology groups

Theorems & Definitions (35)

  • Theorem 1.1
  • Theorem 3.1
  • proof
  • Corollary 3.2
  • proof
  • Proposition 3.3
  • proof
  • Corollary 3.4
  • proof
  • Corollary 3.5
  • ...and 25 more