… Let (R,𝔪) be a complete ring. If R is strongly F-regular and has finite F-representation type.
Suppose that H o m R ( H I i ( R ) , H I i ( R ) ) is a unit R[F e ]-module. Then A n n R ( H o m R ( …

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

… We will show that this category is equivalent to the category of left D-modules. We begin
by explaining how to produce a -divided left D(0)-module from a left D-module. Given a left D-…

… It is then natural to ask which summands of the Fe ∗ R occur as e varies over all of N. If
only finitely many summands occur, we say that R has finite F-representation type, often …

… The main objects of this project are D-modules. We will denote by DA|k the ring of k-linear …
example is given by the ring of k-linear differential operators on the polynomial ring A = k[x1,...,…

… We also present a finiteness result for rings with finite F-representation type, … over Gorenstein
rings with FFRT have finitely many associated primes. We extend this result to all rings …

… We also show that holonomic D-modules, in this context, have finite length. We obtain … over
a field of positive characteristic. Specifically, we work on rings with finite F-representation type…

… The theory of F-signature originates in the following particular case of rings of finite F-representation
type, which was introduced by Smith and Van den Bergh [37] (see …

… D-modules help us gain a better understanding of the structure of local cohomology modules.
For example, D-modules … ideals of a local cohomology module is finite. For the geometric …

… , we prove that the ring of invariants (SymV)G has finite Frobenius representation type. We
also construct an example with V a finite rank vector space over the algebraic closure of the …