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Temperate holomorphic solutions and regularity of holonomic D-modules on curves

Ana Rita Martins
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Abstract

Let $X$ be a complex manifold. In "Microlocal study of Ind-sheaves I: microsupport and regularity", M. Kashiwara e P. Schapira made the conjecture that a holonomic D-module $\shm$ is regular holonomic if and only if $R\mathcal{I}{hom}_{β_X\shd_X}(β_X\shm,\sho_X^t)$ is regular (in the sense of "Microlocal study of Ind-sheaves I: microsupport and regularity"), the "only if" part of this conjecture following immediately from "Microlocal study of Ind-sheaves I: microsupport and regularity". Our aim is to prove this conjecture in dimension one.

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Ana Rita Martins. 2006-02-20. Temperate holomorphic solutions and regularity of holonomic D-modules on curves. https://arxiv.org/abs/math/0602424

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