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arXiv · 1902.08331

Ample line bundles, global generation and $K_0$ on quasi-projective derived schemes

Toni Annala
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Abstract

The purpose of this note is to extend some classical results on quasi-projective schemes to the setting of derived algebraic geometry. Namely, we want to show that any vector bundle on a derived scheme admitting an ample line bundle can be twisted to be globally generated. Moreover, we provide a presentation of $K^0(X)$ as the Grothendieck group of vector bundles modulo exact sequences on any quasi-projective derived scheme $X$.

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Toni Annala. 2019-02-22. Ample line bundles, global generation and $K_0$ on quasi-projective derived schemes. https://arxiv.org/abs/1902.08331

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