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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Functors given by kernels, adjunctions and duality

Author: Dennis Gaitsgory
Journal: J. Algebraic Geom. 25 (2016), 461-548
Published electronically: January 8, 2016
MathSciNet review: 3493590
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Abstract | References | Additional Information

Abstract: Let $X_1$ and $X_2$ be schemes of finite type over a field of characteristic $0$. Let $Q$ be an object in the category $\mathrm {D-mod}(X_1\times X_2)$ and consider the functor $F:\mathrm {D-mod}(X_1)\to \mathrm {D-mod}(X_2)$ defined by $Q$. Assume that $F$ admits a right adjoint also defined by an object $P$ in $\mathrm {D-mod}(X_1\times X_2)$. The question that we pose and answer in this paper is how $P$ is related to the Verdier dual of $Q$. We subsequently generalize this question to the case when $X_1$ and $X_2$ are no longer schemes but Artin stacks, where the situation becomes much more interesting.

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Additional Information

Dennis Gaitsgory
Affiliation: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138

Received by editor(s): June 18, 2013
Received by editor(s) in revised form: August 26, 2013, and November 5, 2013
Published electronically: January 8, 2016
Article copyright: © Copyright 2016 University Press, Inc.