Kashiwara–Schapira's R-constructibility conjecture for tempered solutions

Let XX be a complex manifold, let DX\mathcal{D}_X be its sheaf of differential operators, and let MDhb(DX)\mathcal{M}\in D^b_h(\mathcal{D}_X) be a bounded complex with holonomic cohomology. Write Solt(M)\mathscr{S}ol^t(\mathcal{M}) for its complex of tempered holomorphic solutions on the subanalytic site XsaX_{sa}. Kashiwara–Schapira's conjecture. The complex

Solt(M)\mathscr{S}ol^t(\mathcal{M})

is R\mathbb{R}-sa-constructible. This conjecture describes the image of the tempered solution functor topologically, extending constructibility results for regular holonomic modules; it was proved for complex curves and, in the present article, in full generality.

Sources & referencesView supporting material

Primary source

Giovanni Morando, “Constructibility of tempered solutions of holonomic D-modules”, arXiv:1311.6621 (2013).

Additional references

2 papers in this index state this conjecture (2010–2013). The statement above is taken from the most recent of them; the others are arXiv:1007.4158.

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