Model theory inspired in modern algebraic geometry

• Grant number: 21/06193-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2021
• End date: July 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Hugo Luiz Mariano
• Grantee: Gabriel Bittencourt Rios
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this work, we will study Model Theory from a algebro-geometric approach, that is to say, we will search the literature for the historical use of techniques analogous to schemes in the context of Categorial Model Theory. Centrally, the project will cover Steve Breiner's Ph.D thesis and related articles. Aiming at this, we firstly intend to insert the student in the context of Categorical Logic, with an emphasis on the use of Topoi for the study of Model Theory. Finally, we plan to take Breiner's ideas further: just as sheaves on a topological sapce were generalized to sheaves on a Grothendieck topology, we will try to bring the concept of logical schemes into a more general context. (AU)