The Thursday morning seminar (10:15-11:45 in WSC-N-U-3.05) will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs,…) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.
|on-site / online
|Some topological dynamical systems of number-theoretic origin
|Joachim Hilgert (Paderborn)
|Model categories and pro-$p$ Iwahori-Hecke modules I
|Model categories and pro-$p$ Iwahori-Hecke modules II
|Characterization of open substacks that admit good moduli spaces
|Tannaka duality for algebraic stacks
|Equivariant Artin algebraization and local structure theorems
|Existence of moduli spaces
|Applications to the moduli of vector bundles on a curve
Xucheng Zhang: Characterization of open substacks that admit good moduli spaces, June 2, 2022
For an algebraic stack arising from a moduli problem in algebraic geometry, usually one can find some open substack that admits a (proper) good moduli space, via introducing suitable stability criteria with the help of educated-guessing. However, it would be also interesting to find all open substacks of the algebraic stack that admit proper good moduli spaces. In this talk we provide two examples where all such open substacks can be characterized:
1. Moduli stack of rank 2 vector bundles over a curve.
2. Quotient stack by $\mathbb G_m$.
A major ingredient of the proof is the recent work of Jarod Alper, Daniel Halpern-Leistner and Jochen Heinloth on the existence of good moduli spaces for algebraic stacks.