Derived equivalences over base schemes and support of complexes

2022/08/30 by Max Lieblich, Martin L. Olsson, Lieblich, Max +1 · 1 citation
Mathematics · #14D06 #14D23 #14F08 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2208.14378

openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X and Y be smooth projective varieties over a field k admitting morphisms f:X → T and g:Y → T to a third variety T. We formulate conditions on a derived equivalence Φ:D(X) → D(Y) ensuring that Φ is induced by a complex P ∈ D(X ×_T Y ), defining derived equivalences between the fibers of f and g. We apply our results to the canonical fibration and albanese fibration.

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