Generalizing Neeman's work on bounded t structures on derived perfect categories and derived bounded categories
Generalizing Neeman's work on bounded t structures on derived perfect categories and derived bounded categories
"Generalizing Neeman's work on bounded t structures on derived perfect categories and derived bounded categories", organizado polo CITMAga en formato presencial. Será impartido por Rudradip Biswas (University of Warwick, England).
Data: martes 14 de novembro de 2023
Hora: 16:00 h
Duración: 1 hora
Lugar: Aula 10 da Facultade de Matemáticas USC
Abstract:
I will present some new work (joint with Hongxing Chen, Kabeer Manali Rahul, Chris Parker, and Junhua Zheng) where we generalise Neeman's work by showing that if we take a triangulated category with arbitrary coproducts admitting a single compact generator, and assume that the opposite category of the compacts has finite finitistic dimension (this notion is new from our paper), then the compacts coincide with their completion with respect to a good metric à la Neeman. Neeman had worked with the derived category of quasi-coherent complexes over sufficiently good schemes as the big triangulated category. Our result is a major abstract generalisation of Neeman's because one can "complete" the category of perfect complexes to get the derived bounded category. Neeman also proved that under some reasonably restrictive conditions on the scheme, all bounded t-structures on the derived bounded category of coherent complexes over the scheme are equivalent. This result has also been majorly generalised by us as it follows as a specialisation.