𝐾-theory of line bundles and smooth varieties

Haesemeyer, C.; Weibel, C.

doi:10.1090/proc/14112

$K$-theory of line bundles and smooth varieties
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Proc. Amer. Math. Soc. 146 (2018), 4139-4150 Request permission

Abstract:

We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb {L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X)\cong K_q(\mathbb {L})$ for all $q\le \dim (X)+1$.

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