Let $ k $ be an arbitrary field. We construct examples of regular local $ k $-algebras $ R $(of
positive dimension) for which the ring of differential operators $ D_k (R) $ is trivial in the …

Let R be the coordinate ring of an affine toric variety. We prove, using direct elementary
methods, that the endomorphism ring End R (A), where A is the (finite) direct sum of all …

Finite F-representation type is an important notion in characteristic p commutative algebra,
but explicit examples of varieties with or without this property are few. We prove that a large …

Levasseur and Stafford described the rings of differential operators on various classical
invariant rings of characteristic zero; in each of the cases that they considered, the …

Abstract (EN) In this thesis, we consider two problems related to cocommutative comonoids.
In the first part, we construct an example of a comonoid which is not cocommutative, yet …

By reading a standard formula for the ring of Grothendieck differential operators in a derived
way, we construct a derived (sheaf of) ring of Grothendieck differential operators for …

We study the!-pullback functor and the theory of (relative) D-modules along morphisms of
qcqs schemes p_X: X→ S which are almost of finite presentation and finite tor-amplitude …

Given a polynomial f with coefficients in a field of prime characteristic p, it is known that there
exists a differential operator that raises 1/f to its p th power. We first discuss a relation …

If k is a field and R is a commutative k-algebra, we explore the question of when the ring DR|
k of k-linear differential operators on R is isomorphic to its opposite ring. Under mild …

Commutative algebra has recently witnessed a number of spectacular developments,
resulting in the resolution of long-standing problems. The new techniques and perspectives …