Year: 2026
Type: preprint
Abstract: We define a quadratically enriched pushforward for proper morphisms between smooth, proper Deligne--Mumford stacks over an arbitrary field using Grothendieck--Serre duality. We apply this pushforward to define quadratically enriched Euler classes and Euler numbers of relatively oriented vector bundles on smooth, proper Deligne--Mumford stacks. Finally, we define quadratically enriched fundamental classes for smooth, proper schemes over an arbitrary field, and we use these to propose a definition of quadratically enriched quantum $K$-invariants when the moduli space of stable maps is smooth, tame, and relatively oriented.
Source: arXiv (Cornell University)
Authors: Bethea, Candace, Wickelgren, Kirsten
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213599687