# nLab Lefschetz motive

There exists a motive $\mathbf{L}$, called the Lefschetz motive, such that the motive of the projective line decomposes as

$h(\mathbf{P}^1_k) = h(\Spec(k)) \oplus \mathbf{L}$

Formally inverting the Lefschetz motive in the category of effective pure motives yields the category of pure motives.

Created on May 30, 2013 at 14:02:58. See the history of this page for a list of all contributions to it.