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An introduction to schemes

Grant number: 19/11754-2
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): July 01, 2019
Effective date (End): December 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Carlos Henrique Grossi Ferreira
Grantee:Frederico Rossetto Bianchini
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main goal of the project is to introduce Grothendieck's theory of schemes as an approach to algebraic geometry. The study of classical facts involving affine and projective varieties (as well as of the corresponding pre-requisites of commutative algebra) over algebraically closed fields will serve as a motivation to the necessity of introducing schemes when it comes, say, to algebraic geometry over the ring of rational integers.