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On Noetherian schemes over (C, �, 1) and the category of quasi-coherent sheaves

Banerjee, A (2021) On Noetherian schemes over (C, �, 1) and the category of quasi-coherent sheaves. In: Indiana University Mathematics Journal, 70 (1). pp. 81-119.

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Official URL: https://doi.org/10.1512/iumj.2021.70.8267


Let (C, �, 1) be an abelian, closed symmetric monoidal category satisfying certain conditions, and let X be a scheme over (C, �, 1) in the sense of Toën and Vaquié. In this paper, we show that when X is quasi-compact and semi-separated, any quasi-coherent sheaf on X may be expressed as a filtered colimit of its finitely generated quasi-coherent submodules. Thereafter, we introduce a notion of �field objects� in (C, �, 1) that satisfy several properties similar to those of fields in usual commutative algebra. Finally, we show that the points of a Noetherian and semi-separated scheme X over such a field object K in (C, �, 1) can be recovered from certain kinds of functors between categories of quasi-coherent sheaves. The latter is a partial generalization of some recent results of Brandenburg and Chirvasitu. © 2021 Department of Mathematics, Indiana University. All rights reserved.

Item Type: Journal Article
Publication: Indiana University Mathematics Journal
Publisher: Department of Mathematics, Indiana University
Additional Information: The copyright for this article belongs to Department of Mathematics, Indiana University
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 24 Mar 2021 08:53
Last Modified: 24 Mar 2021 08:53
URI: http://eprints.iisc.ac.in/id/eprint/68528

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