Algebraický seminář

Simone Pizzirani (IM CAS): Compactly generated t-structures over qcqs schemes

Abstract: An interesting problem in tt-geometry is the classification of certain subcategories of, for example, the derived category of a ring or scheme. This gives a strict link between the derived category and the underlying geometry, namely the spectrum of the ring or the scheme itself. Many results exist in this sense, in particular for the case of t-structures. In this talk we will deal with the case of compactly generated t-structures over a qcqs scheme and we will arrive at the classification. To do that, we will first prove that the standard t-structure is compactly generated, using a new tool, called pseudoapproximation, that lets us approximate some bounded above complexes by perfect complexes. This talk is based on joint work with M. Hrbek and P. Lank.