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The Legend of Masaki Kashiwara and Algebraic Analysis

Kiyoshi Takeuchi

Abstract

This survey paper offers a concise introduction to Kashiwara's work on $\mathcal{D}$-modules, microlocal analysis and related subjects. In this way, we explain his role in the development of algebraic analysis.

The Legend of Masaki Kashiwara and Algebraic Analysis

Abstract

This survey paper offers a concise introduction to Kashiwara's work on -modules, microlocal analysis and related subjects. In this way, we explain his role in the development of algebraic analysis.
Paper Structure (6 sections, 9 theorems, 88 equations)

This paper contains 6 sections, 9 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. $\mathcal{D}$-modules
  3. Microlocal analysis
  4. Microlocal study of sheaves
  5. Bernstein-Sato polynomials
  6. Irregular Riemann-Hilbert correspondence

Key Result

Theorem 2.1

The characteristic variety $\mathop{\mathrm{ch}}\nolimits\mathcal{M} \subset T^*X$ of a coherent $\mathcal{D}_X$-module $\mathcal{M}$ is involutive with respect to the canonical symplectic structure of $T^*X$. In particular, for any irreducible component $\Lambda$ of $\mathop{\mathrm{ch}}\nolimits\m

Theorems & Definitions (13)

  • Theorem 2.1
  • Definition 2.2
  • Theorem 2.3
  • Definition 2.4
  • Theorem 2.5
  • Theorem 2.6
  • Definition 4.1
  • Theorem 4.3: Kashiwara-Schapira KS1
  • Theorem 4.5: Kashiwara Kas10 and Kashiwara-Schapira KS2
  • Theorem 5.1: Kashiwara Kas4
  • ...and 3 more