8 papers
The Dolbeault geometric Langlands correspondence for type A groups beyond the elliptic locus
Yukinobu Toda
In this paper, we prove a Dolbeault geometric Langlands equivalence for $\GL_r$ and for the Langlands dual pair $\SL_r/\PGL_r$ over an open locus of the Hitchin base which strictly…
A proof of Dolbeault geometric Langlands for with reduced spectral curves
Yukinobu Toda
In our previous paper with Tudor Pădurariu, we introduced the notion of limit categories for moduli stacks of Higgs bundles and formulated the Dolbeault geometric Langlands corresp…
The Dolbeault geometric Langlands conjecture via limit categories
Tudor Pădurariu, Yukinobu Toda
We introduce limit categories for cotangent stacks of smooth stacks as an effective version of classical limits of categories of D-modules on them. We develop their general theory…
-theoretic pullbacks for Lagrangians on derived critical loci
Yalong Cao, Yukinobu Toda, Gufang Zhao
Given a regular function on a smooth stack, and a -shifted Lagrangian on the derived critical locus of , under fairly general hypotheses, we construct a pullback m…
Topological K-theory of quasi-BPS categories for Higgs bundles
Tudor Pădurariu, Yukinobu Toda
In a previous paper, we introduced quasi-BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the…
Quasi-BPS categories for Higgs bundles
Tudor Pădurariu, Yukinobu Toda
We introduce quasi-BPS categories for twisted Higgs bundles, which are building blocks of the derived category of coherent sheaves on the moduli stack of semistable twisted Higgs b…
Topological K-theory of quasi-BPS categories of symmetric quivers with potential
Tudor Pădurariu, Yukinobu Toda
In previous works, we introduced and studied certain categories called quasi-BPS categories associated to symmetric quivers with potential, preprojective algebras, and local surfac…
Quasi-BPS categories for symmetric quivers with potential
Tudor Pădurariu, Yukinobu Toda
We study certain categories associated to symmetric quivers with potential, called quasi-BPS categories. We construct semiorthogonal decompositions of the categories of matrix fact…