TL;DR
This paper advances the foundation of formal scheme theory by redefining formal schemes as proringed spaces, focusing on non-Noetherian and non-adic cases that have been less explored.
Contribution
It introduces a new definition of formal schemes as proringed spaces and provides initial examples of non-adic formal schemes, expanding the scope of formal scheme theory.
Findings
Redefinition of formal schemes as proringed spaces
Identification of examples of non-adic formal schemes
Analysis of basic properties of non-adic formal schemes
Abstract
Our purpose is to make a contribution to the foundation of the theory of formal scheme. We are interested particularly in non-Noetherian or non-adic formal schemes, which have been little studied. We redefine the formal scheme as a proringed space and study its basic properties. We also find several examples of non-adic formal schemes.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation