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Tensor triangulated category structures in the derived category of a variety with big (anti)canonical bundle

Angel Toledo

Vol. 327 (2023), No. 2, 359–377
Abstract

Let X be a smooth projective variety over with big (anti)canonical bundle. It is known that for such X the Balmer spectrum of the tensor triangulated category of perfect complexes Perf (X), equipped with the derived tensor product X𝕃, recovers the space X. We study the possible tensor triangulated category structures one can put on Perf (X). As an application, we prove a monoidal version of the well-known Bondal–Orlov reconstruction theorem.

Keywords
tensor triangulated category, Balmer spectrum, Bondal–Orlov reconstruction, derived categories
Mathematical Subject Classification
Primary: 14F08, 18G80
Milestones
Received: 23 September 2023
Revised: 28 January 2024
Accepted: 31 January 2024
Published: 12 March 2024
Authors
Angel Toledo
Laboratoire Jean Alexandre Dieudonné
Université Côte d’Azur
Nice
France

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