Kernel algebras and generalized Fourier-Mukai transforms

2008/10/08 by Alexander Polishchuk, Polishchuk, Alexander · 3 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0810.1542

openalex publication_date 2008/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study kernel algebras, i.e., algebras in the category of sheaves on a square of a scheme, where the latter category is equipped with a monoidal structure via a natural convolution operation. We show that many interesting categories, such as D-modules, equivariant sheaves and their twisted versions, arise as categories of modules over kernel algebras. We develop the techniques of constructing derived equivalences between these module categories. As one application we generalize the results of math.AG/9901009 concerning modules over algebras of twisted differential operators on abelian varieties. As another application we recover and generalize the results of Laumon in alg-geom/9603004 concerning an analog of the Fourier transform for derived categories of quasicoherent sheaves on a dual pair of generalized 1-motives.

Cited by

• Categorical Continuous Symmetry
• The Eilenberg-Watts theorem over schemes
• Extensions of Abelian Schemes and the Additive Group

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