… 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 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 …

… , 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 …

… A Drinfeld module has a p-adic Tate module not only for every finite place p of the coefficient
ring … A morphism of (WK , D)-representations is a morphism of underlying D-modules which …

… If F is a p-adic field, V is a de Rham representation of GF over E, and κ : F ֒→ E, then we will
write HTκ(V ) for the multiset of Hodge-Tate weights of V with respect to κ. By definition, HTκ(…

… As an application we conclude that all irreducible finite dimensional representations of Lg,
the … To check that Ff is a well-defined homomorphism of Saff d -modules we note for example …

… ring R has finite F-representation type, then R is F-finite. We collect here some examples of
rings with finite F-representation type… , D-modules over rings with finite F-representation type, …