Holonomic D-modules on abelian varieties
Publications Mathématiques de l'IHÉS, Volume 121 (2015), pp. 1-55.

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”.

DOI: 10.1007/s10240-014-0061-x
Keywords: Line Bundle, Abelian Variety, Coherent Sheave, Coherent Sheaf, Distinguished Triangle
Schnell, Christian 1

1 Department of Mathematics, Stony Brook University 11794 Stony Brook NY USA
     author = {Schnell, Christian},
     title = {Holonomic {D-modules} on abelian varieties},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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Schnell, Christian. Holonomic D-modules on abelian varieties. Publications Mathématiques de l'IHÉS, Volume 121 (2015), pp. 1-55. doi : 10.1007/s10240-014-0061-x.

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