Index theorems for R-constructible sheaves and for D-modules

1993 ◽  
pp. 141-156
Author(s):  
Pierre Schapira ◽  
Jean-Pierre Schneiders
Keyword(s):  
Index Theorems ◽  
Constructible Sheaves ◽  
D Modules

scholarly journals Microlocal Euler classes and Hochschild homology

2013 ◽  
Vol 13 (3) ◽  
pp. 487-516 ◽  
Author(s):  
Masaki Kashiwara ◽  
Pierre Schapira
Keyword(s):  
Cohomology Class ◽  
Cotangent Bundle ◽  
Euler Class ◽  
Hochschild Homology ◽  
Relative Index ◽  
Index Theorems ◽  
Dualizing Complex ◽  
Constructible Sheaves

AbstractWe define the notion of a trace kernel on a manifold $M$. Roughly speaking, it is a sheaf on $M\times M$ for which the formalism of Hochschild homology applies. We associate a microlocal Euler class with such a kernel, a cohomology class with values in the relative dualizing complex of the cotangent bundle ${T}^{\ast } M$ over $M$, and we prove that this class is functorial with respect to the composition of kernels.This generalizes, unifies and simplifies various results from (relative) index theorems for constructible sheaves, $\mathscr{D}$-modules and elliptic pairs.

Tempered solutions of D-modules

2016 ◽  
pp. 39-43
Author(s):  
Masaki Kashiwara ◽  
Pierre Schapira
Keyword(s):  
D Modules
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