Year: 2020
Type: preprint
Abstract: We show the $\mathbb{A}^{1}$-Euler characteristic of a smooth, projective scheme over a characteristic $0$ field is represented by its Hochschild complex together with a canonical bilinear form, and give an exposition of the compactly supported $\mathbb{A}^{1}$-Euler characteristic $χ^{c}_{\mathbb{A}^{1}}: K_0(\mathbf{Var}_{k}) \to \text{GW}(k)$ from the Grothendieck group of varieties to the Grothendieck--Witt group of bilinear forms. We also provide example computations.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: CAREER: Etale and Motivic Homotopy Theory and Applications to Arithmetic Geometry, CAREER: Constructing K-Theoretic Invariants for Geometric Objects, Career Advancement for Women Through Research-Focused Networks, G6230607391, G6671297155, Women in Topology Workshop, Homotopy theory of schemes, Grothendieck's anabelian program, rational points, Graduate Research Fellowship Program (GRFP)
OpenAlex ID: W3012850564