Ir al contenido

Documat


Algebraic foliations and derived geometry: the Riemann–Hilbert correspondence

  • Bertrand Toën [1] ; Gabriele Vezzosi [2]
    1. [1] Université de Toulouse

      Université de Toulouse

      Arrondissement de Toulouse, Francia

    2. [2] Universita di Firenze, Italy
  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 1, 2023
  • Idioma: inglés
  • Enlaces
  • Resumen
    • This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic varieties and on their associated formal and analytic versions. Their truncations are classical singular foliations defined in terms of differential ideals in the algebra of forms. We prove that a quasi-smooth rigid derived foliation on a smooth complex variety X is formally integrable at any point, and, if we suppose that its singular locus has codimension ≥2, its analytification is a locally integrable singular foliation on the associated complex manifold Xh. We then introduce the derived category of perfect crystals on a quasi-smooth rigid derived foliation on X, and prove a Riemann-Hilbert correspondence for them when X is proper. We discuss several examples and applications.


Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno