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”.
@article{PMIHES_2015__121__1_0, author = {Schnell, Christian}, title = {Holonomic {D-modules} on abelian varieties}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {1--55}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {121}, year = {2015}, doi = {10.1007/s10240-014-0061-x}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-014-0061-x/} }
TY - JOUR AU - Schnell, Christian TI - Holonomic D-modules on abelian varieties JO - Publications Mathématiques de l'IHÉS PY - 2015 SP - 1 EP - 55 VL - 121 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://www.numdam.org/articles/10.1007/s10240-014-0061-x/ DO - 10.1007/s10240-014-0061-x LA - en ID - PMIHES_2015__121__1_0 ER -
%0 Journal Article %A Schnell, Christian %T Holonomic D-modules on abelian varieties %J Publications Mathématiques de l'IHÉS %D 2015 %P 1-55 %V 121 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://www.numdam.org/articles/10.1007/s10240-014-0061-x/ %R 10.1007/s10240-014-0061-x %G en %F PMIHES_2015__121__1_0
Schnell, Christian. Holonomic D-modules on abelian varieties. Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 1-55. doi : 10.1007/s10240-014-0061-x. http://www.numdam.org/articles/10.1007/s10240-014-0061-x/
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