On the Involutivity of the Characteristic Variety

Abstract

In this paper, we give a new simple algebraic proof of the involutivity of the characteristic variety after Gabber, which is one of the most important results of D-module theory.

Key Words:

• Characteristic ideal
• Characteristic variety
• Poisson bracket
• Filtered ring

2010 Mathematics Subject Classification:

• Primary 16W70
• Secondary 16W50

ACKNOWLEDGMENT

The authors sincerely thank the referee for very useful comments and suggestions to improve the paper. The authors also thank V. Ginzburg, University of Chicago for his valuable comments concerning Remark 5.2 in this paper. Authors also thank Raja Sridharan (TIFR, Mumbai) and D. S. Nagraj (IMSC, Chennai) for useful discussion.

Notes

Communicated by U. Walther.