I will present some new work 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 abstract generalisation of the concept of finitistic dimension to triangulated categories is nee from our paper), then the compacts coincide with their completion with respect to a good metric in the sense of Neeman. Neeman had worked with the big triangulated category being the derived category of quasi coherent complexes over sufficiently good schemes. 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 had 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 special application of our abstract treatment and it shows that the "restrictive conditions" on the scheme can be eased.
This is joint work with Chris Parker, Kabeer Manali Rahul, Hongxing Chen and Junhua Zhang.

Día

Martes, 14 de novembro de 2023

Lugar

Aula 10
Facultade de Matemáticas