Non-Noetherian representation categories of generalized fields

Abstract

In this paper, we show that the categories of finitely generated projective $\mathbb{B}$-modules and ${\mathbb{F}}_{\infty }$-modules with morphisms being (splittable) injections are not locally Noetherian. This provides another instance of the fact that these generalized fields have strange homological behavior.

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References in corpus (2)

• New Approach to Arakelov Geometry
• Homological algebra in characteristic one