Trivial ring extension: A fresh geometric point of view
Mohamed Aqalmoun
Department of Mathematics, Higher Normal School, Sidi Mohamed Ben Abdellah University, Fez, Morocco.
Pages 315–324 | Received 12 May 2023, Accepted 15 September 2023, Published 11 December 2023
Abstract
Let be a scheme and be a quasi-coherent -module. In this paper we introduce the concept of trivial scheme extension denoted which behave as the trivial ring extension in the affine case, that is is the affine scheme associated to the commutative ring when and is the quasi-coherent module associated to the -module . Two constructions are presented, one of which is based on the gluing of the local data, another construction in terms of quasi-coherent -algebra is considered. Finally we discuss the quasi-affineness of the trivial scheme extension .
Keywords: trivial ring extension, scheme, quasi-coherent module, affine morphism, trivial scheme extension.
MSC numbers: 14A15, 14F06.
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