Year: 2026
Type: article
Abstract: Let A , B be dual abelian varieties. Let B ♮ $B^{\natural }$ upper B Superscript normal ♮ be the universal vectorial extension of B . Laumon and Rothstein independently lift the Fourier–Mukai transform to D A $D_A$ upper D Subscript upper A -modules. They prove that this defines an equivalence of triangulated categories from the derived category D coh b ( D A ) $D_{\mathrm {coh}}^b(D_A)$ upper D Subscript coh Superscript b Baseline left parenthesis upper D Subscript upper A Baseline right parenthesis of coherent D A $D_A$ upper D Subscript upper A -modules to the derived category D coh b ( O B ♮ ) $D_{\mathrm {coh}}^b(O_{B^{\natural }})$ upper D Subscript coh Superscript b Baseline left parenthesis upper O Subscript upper B Sub Superscript normal ♮ Subscript Baseline right parenthesis of coherent sheaves on B ♮ $B^{\natural }$ upper B Superscript normal ♮ . We extend their results to complex tori. As a replacement of coherent algebraic D -modules, we use Kashiwara’s good analytic D -modules. Moreover, to get an equivalence, we have to replace
Source: Nagoya Mathematical Journal
Author: Haohao Liu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7167600317