Idéaux différentiels
Images of locally nilpotent derivations of bivariate polynomial algebras over a domain
We study the LND conjecture concerning the images of locally nilpotent derivations, which arose from the Jacobian conjecture. Let be a domain containing a field of characteristic zero. We prove that, when is a one-dimensional unique factorization domain, the image of any locally nilpotent -derivation of the bivariate polynomial algebra is a Mathieu-Zhao subspace. Moreover, we prove that, when is a Dedekind domain, the image of a locally nilpotent -derivation of with some additional conditions...
Integral differentials and Fermat congruences.
Integration of differential forms on schemes.
Irreducible Jacobian derivations in positive characteristic
We prove that an irreducible polynomial derivation in positive characteristic is a Jacobian derivation if and only if there exists an (n-1)-element p-basis of its ring of constants. In the case of two variables we characterize these derivations in terms of their divergence and some nontrivial constants.