Ample line bundles, global generation and K₀ on quasi-projective\n derived schemes

2019/02/21 by Toni Annala, Annala, Toni
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1902.08331

Abstract

The purpose of this note is to extend some classical results on\nquasi-projective schemes to the setting of derived algebraic geometry. Namely,\nwe want to show that any vector bundle on a derived scheme admitting an ample\nline bundle can be twisted to be globally generated. Moreover, we provide a\npresentation of K⁰(X) as the Grothendieck group of vector bundles modulo\nexact sequences on any quasi-projective derived scheme X.\n

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