Equivalence of bounded t structures on the bounded derived category of coherent sheaves

Rudradip Biswas (University of Warwick)

Tuesday 4th March 15:00-16:00 Maths 311B

Abstract

I will talk about how, on Db_coh(X) for any Noetherian scheme X of finite dimension, all bounded t structures are equivalent in the sense of Neeman, i.e. they are all finite aisle-distance from each other. This result was proved for a few classes of schemes by Neeman himself [Bounded t-structures on the category of perfect complexes, Acta Math. 233 (2024), no. 2, 239–284], but the general case was left as an open question. I will also touch on the problems one faces when the “finite dimension” assumption gets dropped. We will prove a more general categorical result first from which the result for Db_coh(X) will follow as a corollary. Based on: https://arxiv.org/pdf/2401.00130 (the paper is joint with Hongxing Chen, Kabeer Manali Rahul, Chris Parker and Junhua Zheng).

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