Optimal destabilizing centers and equivariant K-stability

作为范畴中心的约化群等变导出范畴

Equivariant derived category of a reductive group as a categorical center

本文证明约化群的伴随等变导出范畴等价于环面等变 Hecke 范畴的 monoidal 中心，并据此重新证明 Drinfeld 中心与幂幺特征层范畴的等价性及强中心层刻画。

Lie groupoid, deformation of unstable curve, and construction of equivariant Kuranishi charts

In this paper we give detailed construction of $G$-equivariant Kuranishi chart of moduli spaces of pseudo-holomorphic curves to a symplectic manifold with $G$-action, for an arbitrary compact Lie group $G$. The proof is based on the deformation theory of {\it unstable} marked curves using the language of Lie groupoid (which is {\it not} necessary etale) and the Riemannnian center of mass technique. This proof is actually similar to [FOn,Sections 13 and 15] except the usage of the language of Lie groupoid makes the argument more transparent. This version correct some errors of the previous vers…

Gieseker 簇的 K-理论与 A 型循环 Hecke 代数

K-theory of Gieseker variety and type A cyclotomic Hecke algebra

本文通过将 Gieseker 空间的等变 K-理论等同于循环 Hecke 代数的 Jucys-Murphy 中心，给出了 Gieseker 簇的等变 K-理论的代数描述，并讨论了其对循环 Hecke 代数中心及 q=1 和单位根特化的影响。

非阿贝尔局部化的范畴视角

A categorical perspective on non-abelian localization

本文从非阿贝尔局部化视角出发，为具有 $Θ$-分层的代数导出栈建立了虚拟 $K$-理论局部化公式及其范畴升级，并据此证明了普适穿墙公式与一维层栈上同调的有限性定理。

Group actions on central simple algebras: a geometric approach

We study actions of linear algebraic groups on central simple algebras using algebro-geometric techniques. Suppose an algebraic group G acts on a central simple algebra A of degree n. We are interested in questions of the following type: (a) Do the G-fixed elements form a central simple subalgebra of A of degree n? (b) Does A have a G-invariant maximal subfield? (c) Does A have a splitting field with a G-action, extending the G-action on the center of A? Somewhat surprisingly, we find that under mild assumptions on A and the actions, one can answer these questions by using techniques from bira…