论文标题
紧凑的支持$ \ mathbb {a}^{1} $ - Euler特征和Hochschild Complex
Compactly supported $\mathbb{A}^{1}$-Euler characteristic and the Hochschild complex
论文作者
论文摘要
我们显示了$ \ mathbb {a}^{1} $ - 特征$ 0 $ field的光滑，投射方案的特征，其Hochschild Complex和典型的双线性形式表示，并提供了紧凑的$ \ MathBb $ \ nathbb {a}^a}^a}^a}^{1} $ euleriantiast of temposect $χ^{c} _ {\ Mathbb {a}^{1}}：k_0（\ MathBf {var} _ {k}）\ to \ to \ text {gw}（k）（k）$，来自Grethendieck of Grothendieck小组，均为Grethendieck-Wittieck-Witeeck--wittieck--wittieck--wittieck--withiteck--withiteck--withiteck--withiteck--withitect-----------------我们还提供示例计算。
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.
