| 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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