Connections on modules over singularities of finite CM representation type

D-modules over Rings with Finite F-representation Type

Smith and Van den Bergh [29] introduced the notion of finite F-representation type as a characteristic p analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if R = L n≥0 Rn is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodi...

Modules with Finite F -representation Type

Finitely generated modules with finite F -representation type (or FFRT for short) over Noetherian (local) rings of prime characteristic p are studied. If a ring R has FFRT or, more generally, if a faithful R-module has FFRT, then tight closure commutes with localizations over R. We also define F -contributors and use them to give an effective way to characterize tight closure. Then we show lime...

Degenerations for Modules over Representation-finite Biserial Algebras

on direct sums of baer modules

the notion of baer modules was defined recently

Big Indecomposable Mixed Modules over Hypersurface Singularities

This research began as an effort to determine exactly which one-dimensional local rings have indecomposable finitely generated modules of arbitrarily large constant rank. The approach, which uses a new construction of indecomposable modules via the bimodule structure on certain Ext groups, turned out to be effective mainly for hypersurface singularities. The argument was eventually replaced by ...