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Holonomic D-modules on abelian varieties

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An Erratum to this article was published on 16 November 2015

Abstract

We study the Fourier-Mukai transform for holonomic D-modules on complex abelian varieties. Among other things, we show that the cohomology support loci of a holonomic D-module are finite unions of linear subvarieties, which go through points of finite order for objects of geometric origin; that the standard t-structure on the derived category of holonomic complexes corresponds, under the Fourier-Mukai transform, to a certain perverse coherent t-structure in the sense of Kashiwara and Arinkin-Bezrukavnikov; and that Fourier-Mukai transforms of simple holonomic D-modules are intersection complexes in this t-structure. This supports the conjecture that Fourier-Mukai transforms of holonomic D-modules are “hyperkähler perverse sheaves”.

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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    Christian Schnell

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  1. Christian Schnell
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Correspondence to Christian Schnell.

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Schnell, C. Holonomic D-modules on abelian varieties. Publ.math.IHES 121, 1–55 (2015). https://doi.org/10.1007/s10240-014-0061-x

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