Perverse pullbacks
Algebraic Geometry
2025-10-21 v1
Abstract
We define a new perverse t-exact pullback operation on derived categories of constructible sheaves which generalizes most perverse t-exact functors in sheaf theory, such as microlocalization, the Fourier-Sato transform and vanishing cycles. This operation is defined for morphisms of algebraic stacks equipped with a relative exact (-1)-shifted symplectic structure, and can be used to define cohomological Donaldson-Thomas invariants in a relative setting. We prove natural functoriality properties for perverse pullbacks, such as smooth and finite base change, compatibility with products and Verdier duality.
Cite
@article{arxiv.2510.16563,
title = {Perverse pullbacks},
author = {Adeel A. Khan and Tasuki Kinjo and Hyeonjun Park and Pavel Safronov},
journal= {arXiv preprint arXiv:2510.16563},
year = {2025}
}
Comments
115 pages