Compactly supported $\mathbb{A}^{1}$-Euler characteristic and the Hochschild complex
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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/24225Collections
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Show full item recordScholars@Duke
Niny Johanna Arcila-Maya
William W. Elliott Assistant Research Professor
Kirsten Graham Wickelgren
Professor of Mathematics
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