Banerjee, Abhishek (2017) Noetherian schemes over abelian symmetric monoidal categories. In: INTERNATIONAL JOURNAL OF MATHEMATICS, 28 (7).
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In this paper, we develop basic results of algebraic geometry over abelian symmetric monoidal categories. Let A be a commutative monoid object in an abelian symmetric monoidal category (C, circle times, 1) satisfying certain conditions and let epsilon(A) = Hom(A-Mod)(A, A). If the subobjects of A satisfy a certain compactness property, we say that A is Noetherian. We study the localization of A with respect to any s epsilon epsilon(A) and define the quotient A/I of A with respect to any ideal I subset of epsilon(A). We use this to develop appropriate analogues of the basic notions from usual algebraic geometry (such as Noetherian schemes, irreducible, integral and reduced schemes, function field, the local ring at the generic point of a closed subscheme, etc.) for schemes over (C, circle times, 1). Our notion of a scheme over a symmetric monoidal category (C, circle times, 1) is that of Toen and Vaquie
| Item Type: | Journal Article |
|---|---|
| Publication: | INTERNATIONAL JOURNAL OF MATHEMATICS |
| Additional Information: | Copy right for this article belongs to the WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 01 Sep 2017 10:19 |
| Last Modified: | 01 Sep 2017 10:19 |
| URI: | http://eprints.iisc.ac.in/id/eprint/57733 |
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