An Introduction to Perfectoid Fields
Ehsan Shahoseini, Soroush Pasandideh
TL;DR
This paper provides an introductory survey of perfectoid fields, covering their motivation, historical context, definitions, and examples to facilitate understanding of this complex area of mathematics.
Contribution
It offers a concise overview of perfectoid fields, highlighting key concepts and examples to aid newcomers in grasping this advanced mathematical topic.
Findings
Defined perfectoid fields and their properties
Presented motivating examples of perfectoid fields
Provided historical background and context
Abstract
This survey is a final project of Twopole DRP in fall 20201. In this paper we try to understand a tiny part of the vast theory of perfecoid spaces, called perfectoid fields. We start by giving some motivation and historical background. Then we define the notion of a perfectoid field and working through some examples.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Algebraic structures and combinatorial models