Given a commutative noetherian ring R we discuss its representations, i.e. its R-modules. The prime spectrum of R plays a fundamental role, controlling much of the structure of the category of R-modules. We illustrate this in two instances, surveying a parametrisation of localising subcategories and a parametrisation of flat ring epimorphisms.
Representations of commutative rings via the prime spectrum
Vitoria, Jorge
2019-01-01
Abstract
Given a commutative noetherian ring R we discuss its representations, i.e. its R-modules. The prime spectrum of R plays a fundamental role, controlling much of the structure of the category of R-modules. We illustrate this in two instances, surveying a parametrisation of localising subcategories and a parametrisation of flat ring epimorphisms.
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