Let $M_R$ be a non-zero‎ ‎module and ${mathcal F}‎: ‎sigma[M_R]times sigma[M_R]‎ ‎rightarrow$ Mod-$Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$mathcal{F}$-reversibility of $M$ is defined by ${mathcal‎ ‎F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎th...

First-principles total energy calculations of the 2-nm clusters seen in high-perfection Al (72)Ni(20)Co(8) decagonal quasicrystals demonstrate that chemical ordering between Al and transition metals in the central ring is energetically highly favorable. The chemical ordering introduces extensive structure relaxation and results in broken decagonal symmetry. Such broken symmetry is sufficient to...

For a prime number p > 2, we give a direct proof of Breuil’s classification of finite flat group schemes killed by p over the valuation ring of a p-adic field with perfect residue field. As application we establish a correspondence between finite flat group schemes and Faltings’s strict modules which respects associated Galois modules via the Fontaine-Wintenberger field-of-norms functor

We prove that every perfect torsion theory for a ring R is differential (in the sense of [2]). In this case, we construct the extension of a derivation of a right R-module M to a derivation of the module of quotients of M . Then, we prove that the Lambek and Goldie torsion theories for any R are differential.

Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of (iso-classes for) indecomposable injective modules are essentially used.

Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective modules are used in an essential way.

Working over perfect ground fields of arbitrary characteristic, I classify minimal normal del Pezzo surfaces containing a nonrational singularity. As an application, I determine the structure of 2-dimensional anticanonical models for proper normal algebraic surfaces. The anticanonical ring may be non-finitely generated. However, the anticanonical model is either a proper surface, or a proper su...

Let (R,m, k) be an excellent, local, normal ring of characteristic p with a perfect residue field and dimR = d. Let M be a finitely generated R-module. We show that there exists β(M) ∈ R such that λ(M/I M) = eHK(M)q d + β(M)q + O(q).

We introduce the concept of the ghost dimension gh. dim. R of a ring R. This is the longest nontrivial chain of maps in the derived category emanating from a perfect complex such that each map is zero on homology. We show that gh. dim. R ≤ w. dim. R, with equality if R is coherent or w. dim. R = 1.

Let R be a perfect Fp-algebra, equipped with the trivial norm. Let W (R) be the ring of p-typical Witt vectors over R, equipped with the p-adic norms. We prove that via the Teichmüller map, the nonarchimedean analytic space (in the sense of Berkovich) associated to R is a (strong) deformation retract of the space associated to W (R).