ON GROUP REPRESENTATIONS OVER A VALUATION RING

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...

Witt group of Hermitian forms over a noncommutative discrete valuation ring

We investigate Hermitian forms on finitely generated torsion modules over a noncommutative discrete valuation ring. We also give some results for lattices, which still are satisfied even if the base ring is not commutative. Moreover, for a noncommutative discrete-valued division algebra D with valuation ring R and residual division algebra D̄, we prove that W(D̄) ∼=WT(R), where WT(R) denotes the ...

Constacyclic Codes over Group Ring (Zq[v])/G

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

Automorphisms of Formal Power Series Rings over a Valuation Ring

The aim of this paper is to report on recent work on liftings of groups of au-tomorphisms of a formal power series ring over a eld k of characteristic p to characteristic 0, where they are realised as groups of automorphisms of a formal power series ring over a suitable valuation ring R dominating the Witt vectors W(k): We show that the lifting requirement for a group of automorphisms places se...

Invariance Group and Invariance Valuation Ring of a Cut