K-theory of line bundles and smooth varieties

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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Published in:Proceedings of the American Mathematical Society 2018-10, Vol.146 (10), p.4139
Main Authors: C. Haesemeyer, C. Weibel
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C. Weibel
description 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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title K-theory of line bundles and smooth varieties
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