Michal Hrbek (MU AVCR): Gluing of t-structures over stalks of affine schemes
Abstract: We show that compactly generated t-structures in the derived category of a commutative ring R correspond bijectively to certain families of compactly generated t-structures over the localizations of R at maximal ideals. These compatible families are given by a natural gluing condition for the associated sequence of Thomason subsets of the Zariski spectrum. As one application, we show that the compact generation of a homotopically smashing t-structure can be checked locally at maximal ideals. Together with a result of Balmer and Favi, this yields that the Telescope Conjecture over a concentrated scheme is a stalk-local property. Furthermore, we show that derived colocalization functors induce a bijection between cosilting objects of cofinite type over R and compatible families of cosilting objects of cofinite type over stalks of R, generalizing the result of Trlifaj and Şahinkaya. This is a report on recent joint work with JiangshengbHu and Rongmin Zhu.
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.