Séminaire d'Homotopie et Géométrie Algébrique

A correspondence between Lie algebroids and foliations in derived algebraic geometry

by Jiaqi Fu (IMT)

IMT 1R2 207 (Salle Pellos)

IMT 1R2 207

Salle Pellos


Infinitesimal derived foliations provide a derived analogue of algebraic foliations in arbitrary characteristics. We use the method of PD Koszul duality to relate infinitesimal derived foliations with partition Lie algebroids, and answer positively a conjecture of Toën and Vezzosi. The comparison theorem implies some formal integrability properties of infinitesimal derived foliations, which might be helpful for the algebraization problem of singular algebraic foliations.