Constructing spectra using cone injectivity

Autor:	Jurka, Jan, Perutka, Tomáš, Vokřínek, Lukáš
Rok vydání:	2022
Předmět:	Mathematics - Category Theory Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	We provide a generalization of the construction of a spectrum of a commutative ring as a locally ringed space, applicable to cone injectivity classes in general contexts, especially in locally finitely presentable categories. In its full generality, the spectrum functor fails to be fully faithful and we study reasonable sufficient conditions under which it is. Further, assuming the full faithfulness, we introduce a generalization of another concept from algebraic geometry -- the functor of points -- and prove equivalence of the two resulting notions of schemes. Comment: minor changes - mainly just improved readability
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.03516 Zobrazit plný text záznamu View this record from Arxiv