Leonid Positselski (MI, CAS)
Derived adically complete modules and complexes
Abstract: Let I be a finitely generated ideal in a commutative ring R. Several definitions of derived I-adically complete complexes of R-modules exist in the literature. I will explain that there are, in fact, three reasonable triangulated categories of derived I-adically complete complexes arising from two abelian categories of derived I-adically complete R-modules. There are also two triangulated categories of derived I-torsion complexes related to one abelian category of I-torsion R-modules. When the ideal I is weakly proregular (in particular, when the ring R is Noetherian), there is only one category in each case.
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.