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Compactly supported $\mathbb{A}^{1}$-Euler characteristic and the Hochschild complex Arcila-Maya, Niny Bethea, Candace Opie, Morgan Wickelgren, Kirsten Zakharevich, Inna 2022-01-24T20:16:03Z 2022-01-24T20:16:03Z 2020-03-20
dc.description.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 $\chi^{c}_{\mathbb{A}^{1}}: K_0(\mathbf{Var}_{k}) \to \text{GW}(k)$ from the Grothendieck group of varieties to the Grothendieck--Witt group of bilinear forms. We also provide example computations.
dc.subject math.AG
dc.subject math.AG
dc.subject 14F42 (Primary), 19E15, 13D03, 55M05 (Secondary)
dc.title Compactly supported $\mathbb{A}^{1}$-Euler characteristic and the Hochschild complex
dc.type Journal article Arcila-Maya, Niny|1200165 Wickelgren, Kirsten|0977513 2022-01-24T20:16:02Z
pubs.organisational-group Duke
pubs.organisational-group Trinity College of Arts & Sciences
pubs.organisational-group Mathematics
duke.contributor.orcid Arcila-Maya, Niny|0000-0003-4696-8415

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