FPU2025 - Arithmetic Geometry

There are many possible PhD projects in Arithmetic Geometry, supervised by Daniel Macías Castillo. Please contact me by email for a more concrete discussion. Arithmetic Geometry studies both number fields and function fields of curves over finite fields, and rational points on varieties defined over such fields, or even on Galois representations. This study relates them to special L-values. An important example is the Birch and Swinnerton-Dyer Conjecture for elliptic curves or abelian varieties. A possible PhD problem is to investigate this conjecture through the ideas of Iwasawa theory. Recently there has also been much interest in Drinfeld modules over global functions fields, a source of Galois representations and L-values in positive characteristic. There are also many possible PhD problems in this new and exciting direction.