Virtual Localization in equivariant Witt cohomology

TL;DR

This paper extends the virtual localization theorem to equivariant Witt cohomology under a specific group action, replacing Chow groups with Witt sheaf cohomology, advancing algebraic geometry techniques.

Contribution

It introduces a new localization theorem in equivariant Witt cohomology for actions by the normalizer of the torus in SL_2, with twisted Witt sheaf cohomology.

Findings

Proves an analog of the Graber-Pandharipande localization theorem

Establishes localization in equivariant Witt cohomology

Replaces Chow groups with Witt sheaf cohomology in the theorem

Abstract

We prove an analog of the virtual localization theorem of Graber-Pandharipande, in the setting of an action by the normalizer of the torus in $\text{SL}_2$, and with the Chow groups replaced by the cohomology of a suitably twisted sheaf of Witt groups.