Graded rings associated to valuations and their relations to tame and deeply ramified fields

• Grant number: 23/04651-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: March 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Josnei Antonio Novacoski
• Grantee: Caio Henrique Silva de Souza
• Supervisor: Mark Spivakovsky
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Université Paul Sabatier - Toulouse III, France
• Associated to the scholarship: 21/13531-0 - Graded rings associated to limit key polynomials, BP.DR

Abstract

The main goal of this research project is to study the graded ring associated to a valuation and its relations with special classes of fields: the tame fields and deeply ramified fields. This is a natural continuation for the Master's project of the candidate, supported by FAPESP (process number 2020/05148-0), and is a complement to his current Ph.D. project (process number 2021/13531-0). Furthermore, the objects of interest of this project are related to the programs for constructing local uniformization (the local form of resolution of singularities for algebraic varieties) in positive characteristic. This is strongly related to the research area of both the supervisor and the co-supervisor of this project. (AU)