Stratified order one differential equations in positive characteristic

Marius Put, van Der (1) , Jaap Top (1)

1 Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence

Stratification for nonlinear differential equations in positive characteristic is introduced. Testing this notion for first order equations is discussed, and related to the Cartier operator on curves. A variant of the Grothendieck-Katz conjecture is formulated, and proved in a special case.

Domaines: Géométrie algébrique [math.AG]

Marius Put, van Der, Jaap Top. Stratified order one differential equations in positive characteristic. MEGA'2013 (Special Issue), Jun 2013, Frankfurt am Main, Allemagne. ⟨hal-01022887⟩