Frau D’zoara Núñez

Algebra und Zahlentheorie

Team

az.uni-wuppertal.de/de/personen/dzoara-nunez-ramos/

Biografie

PhD in Mathematics, 2023–present:

                Supervised by Prof. Dr. Kay Rülling and Prof. Dr. Stefan Schröer

                Bergische Universität Wuppertal and Heinrich-Heine-Universität Düsseldorf

                Funded through the DFG Research Training Group 2240 "Algebro-Geometric Methods 
                in Algebra, Arithmetic and Topology''

 

Master in Mathematics, 2021–2023:

               Supervised by Prof. Dr. Germán Benítez and Prof. Dr. Wolfgang Bock 

               Universidade Federal do Amazonas, Brazil

 

Bachelor in Mathematics, 2013–2021: 

                Supervised by Prof. Dr. Verónica Cifuentes and Prof. Dr. Pedro Hernández 

                Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

 

Titel und Abstract des Dissertationsprojekts:

Resolution and Cohomology of a Moderately Ramified Quotient Singularity

Let $k$ be an algebraically closed field. In characteristic 2, isolated wild quotient singularities arising from an action of the cyclic group $\mathbb{Z}\slash 2 \mathbb{Z}$ on the power series ring $k \llbracket u,v\rrbracket$ were explicitly described by Artin as hypersurface singularities. Peskin later extended this result to characteristic 3. More recently, Schröer and Lorenzini introduced the notion of moderately ramified actions in arbitrary characteristic $p>0$, producing a new class of wild quotient singularities. 

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Motivated by this framework, we describe a resolution of singularities of a specific example arising from a moderately ramified action on $k \llbracket u,v\rrbracket$ in arbitrary characteristic. We then compute the cohomology of the structure sheaf of the resolution, which provides a concrete cohomological invariant of the singularity.

 

Sonstige wissenschaftliche Aktivitäten/Mitgliedschaften:

Member of the GRK 2240: Algebro-Geometric Methods in Algebra, Arithmetic and Topology