K-theory of line bundles and smooth varieties

2017/07/05 by Christian Haesemeyer, Haesemeyer, Christian, Charles A. Weibel +1
Mathematics · Physics and Astronomy · #14F20 #19D55 #19E08 #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1707.01192

openalex publication_date 2017/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a K-theoretic criterion for a quasi-projective variety to be smooth. If \mathbbL is a line bundle corresponding to an ample invertible sheaf on X, it suffices that K_q(X) = K_q(\mathbbL) for all q≤dim(X)+1.

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