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Modules of minimal dimension over completed Weyl algebras

Feliks Rączka

Abstract

We study the category of modules of minimal dimension over completed Weyl algebras in equal characteristic zero. In particular we prove finiteness of de Rham cohomology of such modules.

Modules of minimal dimension over completed Weyl algebras

Abstract

We study the category of modules of minimal dimension over completed Weyl algebras in equal characteristic zero. In particular we prove finiteness of de Rham cohomology of such modules.
Paper Structure (9 sections, 10 theorems, 53 equations)

This paper contains 9 sections, 10 theorems, 53 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Modules of minimal dimension
  4. Completed Weyl Algebras
  5. Algebras over discrete valuation rings
  6. Künneth type short exact sequences
  7. Reduction of lattices
  8. Euler characteristic of a perfect complex over a complete discrete valuation ring
  9. Proof of Theorem \ref{['MainThm1']}

Key Result

Theorem 1.1

Let $K$ be a discretely valued nonarchimedean field of equal characteristic zero and let $M$ be a left ${\widehat{\mathcal{D}}}_{n}$-module of minimal dimension. Then $\dim_{K}H^{i}_{dR}(M)<\infty$ for all $i$.

Theorems & Definitions (19)

  • Theorem 1.1
  • Theorem 1.2
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • ...and 9 more