The Dolbeault geometric Langlands conjecture via limit categories
演讲者
Yukinobu Toda
时间
2025年10月30日 15:00 至 16:00
地点
A6-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
In this talk, I will introduce the notion of limit categories for cotangent stacks of smooth stacks as an effective version of classical limits of the categories of D-modules on them. Using the notion of limit categories, I will propose a precise and tractable formulation of the Dolbeault geometric Langlands conjecture, proposed by Donagi–Pantev as the classical limit of the geometric Langlands correspondence. It states an equivalence between the derived categories of coherent sheaves on moduli stacks of semistable G-Higgs bundles for a reductive group G and the limit category of moduli stacks of G^L-Higgs bundles without a stability condition. I will show the existence of a semiorthogonal decomposition of the limit category into quasi-BPS categories, which (when G=GL_r) categorify BPS invariants on a non-compact Calabi–Yau 3-fold playing an important role in Donaldson-Thomas theory. This semiorthogonal decomposition is interpreted as a Langlands dual to the semiorthogonal decomposition for moduli stacks of semistable Higgs bundles, obtained in our earlier work as a categorical analogue of PBW theorem in cohomological DT theory. It in particular yields a conjectural equivalence between quasi-BPS categories, which gives a categorical version of Hausel-Thaddeus mirror symmetry for Higgs bundles (for any G), This is a joint work with Tudor Pădurariu.