Comparison between the different programs for local uniformization

• Grant number: 15/23409-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2016
• End date: August 14, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Daniel Levcovitz
• Grantee: Josnei Antonio Novacoski
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main goal of this research project is to compare the programs developed by Spivakovsky, by Teissier and by Knaf and Kuhlmann to solve the local uniformization problem in positive characteristic. Some of the specific problems that will be studied are the following: * Stablish the relation between key polynomials and pseudo-convergent sequences; *Study the effect of differential operators on key polynomials; * Understand the role of the graded ring of a valuation to the local uniformization problem; * Study extensions of valuation rings which are essentially finitely generated; * Research the equivalent of the Hironaka's game in the programs of Teissier and of Knaf and Kuhlmann; * Continue the studies on the valuative tree and in spaces of valuations. Part of this project is a natural continuation of the work developed during the post-doctoral studies of the candidate at University Paul Sabatier-Toulouse III.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

NOVACOSKI, JOSNEI; SPIVAKOVSKY, MARK. Key polynomials and pseudo-convergent sequences. Journal of Algebra, v. 495, p. 199-219, FEB 1 2018. (15/23409-7)

NOVACOSKI, JOSNEI. Key polynomials and minimal pairs. Journal of Algebra, v. 523, p. 1-14, APR 1 2019. (17/17835-9, 15/23409-7)