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Ind-Sheaves, distributions, and microlocalization

Masaki Kashiwara·Pierre Schapira
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Abstract

This is an announcement of a long paper in progress. On a locally compact space, we introduce the stack of ind-sheaves (ind-objects of the category of sheaves with compact support) and construct the analogous of the usual six operations on sheaves. As an application, we treat, in the formalism of ind-sheaves, functions with growth conditions such as the ``tempered holomorphic functions'' on a complex manifold. We also construct a microlocalization functor from the category of sheaves on a manifold to that of ind-sheaves on the cotangent bundle.

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Masaki Kashiwara, Pierre Schapira. 1999-06-29. Ind-Sheaves, distributions, and microlocalization. https://arxiv.org/abs/math/9906200

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