Algebra seminar

Current seminar:
Monday, June 8, 15:30–18:00, via ZOOM (the address of the meeting will be sent to you by email a couple of minutes earlier)

15:30 - Jordan Williamson (Univ. Sheffield): Algebraic models for change of groups functors

17:00 - Leonid Positselski (IM CAS, Prague): A construction of complete cotorsion pairs in the relative context

Abstract (Jordan Williamson): Equivariant cohomology theories are powerful invariants of spaces with the action of a group. A conjecture of Greenlees states that when one restricts to the equivariant cohomology theories taking values in rational vector spaces, there is an abelian category equivalent to it. This conjecture has been proven in many cases; for example for finite groups, for tori of any rank, or for equivariant cohomology theories on spaces with a free action. The inclusion of a subgroup H into a compact Lie group G induces an adjoint triple of induction, restriction and coinduction functors between the categories of G-equivariant cohomology theories and
H-equivariant cohomology theories, analogous to the functors in representation theory. In this talk, I will explain how to connect the induction, restriction and coinduction functors in topology with functors in algebra. I will attempt to focus on the more algebraic aspects of this story, in particular, the Gorenstein condition in derived commutative algebra context.
Abstract (Leonid Positselski): Let R -> A be a ring homomorphism, and let (F,C) be a hereditary complete cotorsion pair in R-Mod. Let (F_A,C_A) be the cotorsion pair in A-Mod for which F_A is the class of all A-modules whose underlying R-modules belong to F. Assuming that countable products of modules from F have finite F-resolution dimension bounded by a natural number k and the class F is preserved by the functor Hom_R(A,-), we show that C_A is the class of all direct summands of A-modules cofiltered by A-modules coinduced from modules from C, with the cofiltrations indexed by the ordinal omega+k.

Previous program:

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.