Scholarship 21/11246-7 - Valorizações, Anéis e álgebras comutativos - BV FAPESP
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Advances in the problem of local uniformization in positive characteristic

Grant number: 21/11246-7
Support Opportunities:Scholarships abroad - Research
Start date: May 01, 2022
End date: October 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Josnei Antonio Novacoski
Grantee:Josnei Antonio Novacoski
Host Investigator: 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  

Abstract

The local uniformization problem is the local form of resolution of singularities for algebraic varieties. Both problems of resolution of singularities and local uniformization were proven in characteristic zero. However, both problems are open in the complementary case of positive characteristic. The main goal of this project is to deepen the knowledge about the local uniformization in positive characteristic. To this end, it is necessary to have a more detailed understanding of some related objects. Some of these objects are key polynomials, Newton polygons and the graded algebra associated to a valuation. We obtained recently, important results for a better understanding of these objects. This research project will be crucial to share these results with the main research groups in this area in Europe. We hope that this interaction will allow us to obtain more general results in the direction of a complete proof of local uniformization. (AU)

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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)
NART, ENRIC; NOVACOSKI, JOSNEI. Geometric parametrization of valuations on a polynomial ring in one variable. MATHEMATISCHE ZEITSCHRIFT, v. 304, n. 4, p. 21-pg., . (21/11246-7, 17/17835-9)
NART, ENRIC; NOVACOSKI, JOSNEI. The defect formula. ADVANCES IN MATHEMATICS, v. 428, p. 44-pg., . (21/11246-7, 17/17835-9)