Coloquio Junior de matemáticas
A primer on F-singularities
Ponente: Adrián Santos Quiles (Universidad Autónoma de Madrid)Fecha: martes 28 de abril de 2026 - 17:00 (coffe break a las 18:00)Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
The study of singular algebraic varieties is a rich and long-standing topic in algebraic geometry, finding deep connections to birational geometry and commutative algebra. In prime characteristic, motivated by Kunz's celebrated theorem (1969) that characterizes regularity in terms of the flatness of the Frobenius map, significant effort has been devoted to analyzing the behaviour of the Frobenius map on singular varieties. This has ultimately led to the development of the theory of \(F\)-singularities, many ideas of which originate from the foundational work of Hochster and Huneke on tight closure in the 1990s. The aim of this talk will be to give a gentle introduction to this family of singularities, highlighting their relevance in different contexts and establishing relationships and parallelisms with the singularities studied in the classical characteristic zero setting.
