Arithmetic of Shimura Varieties

  • Laurent Fargues

    Université de Paris VI, Paris, France
  • Ulrich Görtz

    Universität Essen, Germany
  • Eva Viehmann

    TU München, Garching, Germany
  • Torsten Wedhorn

    Technische Universität Darmstadt, Germany

Abstract

Arithmetic properties of Shimura varieties are an exciting topic which has roots in classical topics of algebraic geometry and of number theory such as modular curves and modular forms. This very active research field has contributed to some of the most spectacular developments in number theory and arithmetic geometry in the last twenty years. Shimura varieties and their equal characteristic analogue, moduli spaces of shtukas, are closely related to the Langlands program (classical as well as p-adic). A particular case is given by moduli spaces of abelian varieties, a classical object of study in algebraic geometry.

Cite this article

Laurent Fargues, Ulrich Görtz, Eva Viehmann, Torsten Wedhorn, Arithmetic of Shimura Varieties. Oberwolfach Rep. 16 (2019), no. 1, pp. 65–131

DOI 10.4171/OWR/2019/2