Classification theorems for $p$-groups and modules over a discrete valuation ring

A Classification of Modules over Complete Discrete Valuation Rings

Fano Fibrations over a Discrete Valuation Ring

Using the Log minimal model program we construct nice models of del Pezzo fibrations which are relevant to the inductive study of del Pezzo fibrations. To investigate birational maps of Fano fibrations, we study elements in anticanonical linear systems of Fano varieties, which have the “worst” singularities. We also investigate certain special points on smooth hypersurfaces of degree n ≥ 3 in P...

Filtered Modules over Discrete Valuation Domains

We consider a uni ed setting for studying local valuated groups and coset-valuated groups, emphasizing the associated ltrations rather than the values of elements. Stable exact sequences, projectives and injectives are identi ed in the encompassing category, and in the category corresponding to coset-valuated groups.

The Stability Classification for Abelian-by- Finite Groups and Modules over a Group Ring

Let G be a finite group. We consider the question: what are the superstable and co-stable abelian-by-G groups? (We consider these as structures in a suitable first order language, see § 1). We see that it is equivalent to ask: what are the superstable and co-stable Z[G]-modules? If we wish our answer to be such as to provide, at least in principle, some sort of uniform listing of all the (say) ...

Dual Modules over a Valuation