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- Tags: - #todo/untagged - Refs: - #todo/add-references - Links: - derived stack - K theory in AG - weighted point count

Lefschetz motive

• \({\mathbb{L}}= [{\mathbf{A}}^1_{/ {k}} ]\) is the Lefschetz motive and \({\mathbb{T}}= {\mathbb{L}}^{-1}\) is the Tate motive, its tensor inverse.

\begin{align*} {\mathbf{Z}}(1) \coloneqq M{\mathbf{Z}}_X \wedge\Sigma^\infty ({\mathbf{P}}^1, \left\{{\infty}\right\})[-2] \qquad \in {\mathsf{DM}}(X) \end{align*}