Test ideals were first introduced by Mel Hochster and Craig Huneke in their celebrated
theory of tight closure, and since their invention have been closely tied to the theory of …

At least since Habousch's proof of Kempf's vanishing theorem, Frobenius splitting
techniques have played a crucial role in geometric representation theory and algebraic …

We prove that the F-jumping numbers of the test ideal τ (X; Δ, a^ t) are discrete and rational
under the assumptions that X is a normal and F-finite scheme over a field of positive …

Let R be a commutative ring containing a field of characteristic p> 0. The Frobenius map F:
R→ R is a ring homomorphism sending x to xp for each x∈ R. The letter “F” in the title of this …

We study the structure of D-modules over a ring R which is a direct summand of a
polynomial or a power series ring S with coefficients over a field. We relate properties of D …

This paper investigates the existence and properties of a Bernstein–Sato functional equation
in nonregular settings. In particular, we construct D-modules in which such formal equations …

151 Rings of Frobenius operators Page 1 Math. Proc. Camb. Phil. Soc. (2014), 157, 151–167
c Cambridge Philosophical Society 2014 doi:10.1017/S0305004114000176 First published …

We study the behavior of various properties of commutative Noetherian rings under Segre
products, with a special focus on properties in positive prime characteristic defined using the …

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 …

Let $ R $ be a commutative Noetherian ring of prime characteristic $ p $. In this paper, we
give a short proof using filter regular sequences that the set of associated prime ideals of …