Nearby motivic sheaves of weighted equivariant functions

• 成果类型: Article
• 署名作者: Ivorra, Florian; Sebag, Julien
• 署名单位: Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01174-1
• 发表日期: 2023
• 页码: 833-862
• 关键词: donaldson-thomas invariants; characteristic zero; monodromy; Algebra; quiver; field; hopf

摘要

Let k be a field of characteristic zero and let X be an algebraic k-variety endowed with an action of the multiplicative algebraic monoid A(1). In this article, we prove that the nearby motivic sheaf functor of a weighted A(1)-equivariant function on X commutes with direct (and exceptional direct) images when applied to constant objects and their twists by Thom spaces of equivariant vector bundles. This proves a generalized categorified version of the conjectures of Behrend-Bryan-Szendro?i and Davison-Meinhardt in the context of motivic stable homotopy theory. In particular, our formula is functorial, holds for general weighted A(1)-equivariant functions and provides, as a direct consequence, a positive answer to the conjectures of Behrend- Bryan-Szendro?i and Davison-Meinhardt for virtual motives.