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Tokyo-Nagoya Algebra Seminar
Seminar information archive ～06/13｜Next seminar｜Future seminars 06/14～
| Organizer(s) | Noriyuki Abe, Aaron Chan, Osamu Iyama, Yasuaki Gyoda, Hiroyuki Nakaoka, Ryo Takahashi |
|---|
2026/06/10
16:30-18:00 Online
Calvin Pfeifer (University of Cologne)
Generic modules arising from stability (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Calvin Pfeifer (University of Cologne)
Generic modules arising from stability (English)
[ Abstract ]
This talk is a report on joint work in progress with Lidia Angeleri-Hügel and Rosanna Laking. Our aim is to extend parts of the theory of large modules over tame hereditary algebras to arbitrary tame algebras.
Let A be a tame finite dimensional algebra over an algebraically closed field, and θ an additive functional on the Grothendieck group of A. Baumann, Kamnitzer and Tingley associate to θ a wide interval in the lattice of torsion classes of the category of finite dimensional A-modules, whose corresponding wide subcategory consists of the θ-semistable A-modules in the sense of King. Angeleri-Hügel, Laking and Sentieri use cosilting theory to assign to such a wide interval a closed rigid subset of the Ziegler spectrum of the unbounded derived category of all A-modules. On the other hand, Plamondon associates to θ a generically $τ^-$-regular irreducible component of the scheme of A-modules. In this talk, we will explain how the closed rigid subset of the Ziegler spectrum is determined by generic modules constructed from the generically $τ^-$-regular irreducible component.
Zoom ID 839 3959 5057
password 518784
[ Reference URL ]This talk is a report on joint work in progress with Lidia Angeleri-Hügel and Rosanna Laking. Our aim is to extend parts of the theory of large modules over tame hereditary algebras to arbitrary tame algebras.
Let A be a tame finite dimensional algebra over an algebraically closed field, and θ an additive functional on the Grothendieck group of A. Baumann, Kamnitzer and Tingley associate to θ a wide interval in the lattice of torsion classes of the category of finite dimensional A-modules, whose corresponding wide subcategory consists of the θ-semistable A-modules in the sense of King. Angeleri-Hügel, Laking and Sentieri use cosilting theory to assign to such a wide interval a closed rigid subset of the Ziegler spectrum of the unbounded derived category of all A-modules. On the other hand, Plamondon associates to θ a generically $τ^-$-regular irreducible component of the scheme of A-modules. In this talk, we will explain how the closed rigid subset of the Ziegler spectrum is determined by generic modules constructed from the generically $τ^-$-regular irreducible component.
Zoom ID 839 3959 5057
password 518784
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
