arXiv subjects
Publications and source records attributed to Bhamidi Sreedhar.
We establish a Hirzebruch-Riemann-Roch type theorem and Grothendieck-Riemann-Roch type theorem for matrix factorizations on quotient Deligne-Mumford stacks. For this we first construct a Hochschild-Kostant-Rosenberg type isomorphism explicit enough to yield a categorical Chern character formula. We next find an expression of the canonical pairing of Shklyarov under the isomorphism.
For a $G$-scheme $X$ with a given equivariant perfect obstruction theory, we prove a virtual equivariant Grothendieck-Riemann-Roch formula, this is an extension of a result of Fantechi-Göttsche to the equivariant context. We also prove a virtual non-abelian localization theorem for schemes over $\mathbb{C}$ with proper actions.
We prove an Atiyah-Segal isomorphism for the higher $K$-theory of coherent sheaves on quotient Deligne-Mumford stacks over $\C$. As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an isomorphism between the higher $K$-theory of coherent sheaves on a Deligne-Mumford stack and the higher Chow groups of its inertia stack. Furthermore, this isomorphism is covariant for proper maps between Deligne-Mumford stacks.
B. Kim and the first author proved a result comparing the virtual fundamental classes of the moduli spaces of stable quasimaps and stable LG-quasimaps by studying localized Chern characters for 2-periodic complexes. In this paper, we study a K-theoretic analogue of the localized Chern character map and show that for a Koszul 2-periodic complex it coincides with the cosection localized Gysin map by Y.-H. Kiem and J. Li. As an application we compare the virtual structure sheaves of the moduli space of stable quasimaps and stable LG-quasimaps.