Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Algebraic integrable connections with bounded irregularity

Takuro Mochizuki

Abstract

We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic $D$-modules with dominated characteristic cycles.

Algebraic integrable connections with bounded irregularity

Abstract

We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic -modules with dominated characteristic cycles.
Paper Structure (198 sections, 191 theorems, 259 equations)

This paper contains 198 sections, 191 theorems, 259 equations.

Table of Contents

  1. Introduction
  2. Boundedness
  3. Boundedness for coherent sheaves
  4. Boundedness for meromorphic flat bundles
  5. Boundedness for holonomic $\mathcal{D}$-modules with dominated characteristic cycles
  6. Good meromorphic flat bundles
  7. Good set of ramified irregular values
  8. Good meromorphic flat bundles
  9. Boundedness of good meromorphic flat bundles as meromorphic objects
  10. Resolution of turning points
  11. Resolutions and boundedness
  12. Outline for Theorem \ref{['thm;26.2.23.20']}
  13. Meromorphic Lagrangian covers
  14. Wild harmonic bundles
  15. The associated meromorphic objects
  16. ...and 183 more sections

Key Result

Theorem 1.1

There exists a smooth complex variety $\mathcal{S}_1$ and a coherent torsion-free $\mathcal{O}_{\mathcal{S}_1\times X}$-module $E_{\mathcal{S}_1}$ with a meromorphic integrable connection relative to $\mathcal{S}_1$ such that the following holds.

Theorems & Definitions (258)

  • Theorem 1.1
  • Theorem 1.2
  • Remark 1.3
  • Corollary 1.4
  • Theorem 1.5: Theorem \ref{['thm;25.12.14.20']}, Lemma \ref{['lem;26.2.24.1']}
  • Definition 1.6
  • Remark 1.7
  • Remark 1.8
  • Theorem 1.9: Theorem \ref{['thm;25.10.15.40']}
  • Theorem 1.10
  • ...and 248 more