Tensor functors between categories of quasi-coherent sheaves

JOURNAL OF ALGEBRA

卷:399

Article

Brandenburg, Martin¹  Chirvasitu, Alexandru² 

[1] Westfalische Wilhelms Univ Munster, Fachbereich Math & Informat, Munster, Germany

[2] Univ Calif Berkeley, Berkeley, CA 94720 USA

关键词: Quasi-compact;    Quasi-separated;    Tensor functor;    Tannaka reconstruction;   

DOI  :  10.1016/j.jalgebra.2013.09.050

来源: Elsevier

【 摘 要 】

For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction f bar right arrow f* implements an equivalence between the discrete category of morphisms Y -> X and the category of cocontinuous tensor functors Qcoh(X) -> Qcoh(Y). This is an improvement of a result by Lurie and may be interpreted as the statement that algebraic geometry is 2-affine. Moreover, We prove the analogous version of this result for Durov's notion of generalized schemes. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free