Fourier–Mukai transform for sheaves with connection on complex tori

Le résumé fourni par la source

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

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