The defect of an extension of valued fields

• Grant number: 22/14876-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 12, 2023
• End date: February 25, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Josnei Antonio Novacoski
• Grantee: Josnei Antonio Novacoski
• Visiting researcher: Mark Spivakovsky
• Visiting researcher institution: Université Paul Sabatier - Toulouse III , France
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• City of the host institution: São Carlos
• Associated research grant: 17/17835-9 - The relation between toric geometry, theory of local blow-ups and ramification theory and their applications in valuation theory, AP.JP

Abstract

The main goal of this visit is to continue the collaboration on the defect of an extension of valued fields. The defect is one of the main obstacles for local uniformization (and resolution of singularities) in positive characteristic. Recently, the researchers involved in this project made expressive developments for a better understanding of the defect. This visit will serve to continue the research on this topic.It is important to emphasize that various researchers in DM-UFSCar and ICMC-USP will benefit from this visit. For instance, in the previous visits, Spivakovsky interacted in a effective way with some graduate students in the DM-UFSCar. Also, he had many discussions with members of different groups of research, for example in singularity theory. (AU)