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.
Full text not available from this repository.Abstract
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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