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...

In the title compound, C(18)H(14)N(2)O(4), the dihedral angle between the benzene ring and the naphthyl ring system is 10.1 (2)°. The mol-ecule is nearly planar, with a mean deviation from the plane of 0.141 (2) Å for 24 non-H atoms. An intra-molecular O-H⋯N hydrogen bond forms a pseudo-6-membered ring and the mol-ecules are linked into sheets by inter-molecular N-H⋯O and O-H⋯O hydrogen bonds.

In this paper, we aim to study valuations on finite extensions of Q. These extensions fall under a special type of field called a global field. We shall also cover the topics of the Approximation Theorems and the ring of adeles, or valuation vectors.

Let V be a complete discrete valuation ring of mixed characteristic. We classify arithmetic D-modules on Spf(V[[t]]) up to certain kind of ‘analytic isomorphism’. This result is used to construct canonical extensions (in the sense of Katz and Gabber) for objects of this category.

In the title compound, C15H19N3O2, the piperazine ring adopts a chair conformation, with its N-C bonds in pseudo-equatorial orientations. The dihedral angle between the C atoms of the piperazine ring and the phthalamide ring system (r.m.s. deviaiton = 0.008 Å) is 89.30 (8)°. In the crystal, mol-ecules are linked by C-H⋯O hydrogen bonds, generating a three-dimensional network and aromatic π-π in...

In the title compound, C22H19N3O3S, the six-membered ring of the 1,2,3,4-tetra-hydro-naphthalene ring system adopts an envelope conformation with the central CH2 C atom as the flap. The mol-ecular conformation is stabilized by an S⋯O contact, forming a pseudo-five-membered ring. In the crystal, mol-ecules are linked via C-H⋯O hydrogen bonds into chains propagating along [102].

In the title compound, C(11)H(12)N(2)O(4), a new hydroxamic acid which belonging to the isoquinole family, the heterocyclic ring adopts a half-chair conformation. The nitro group is essentially coplanar with the aromatic ring. Inter-molecular O-H⋯O hydrogen bonds assemble the mol-ecules around inversion centres to form pseudo-dimers.

In this paper we construct a natural category ~r of locally and topologically ringed spaces which contains both the category of locally noetherian formal schemes and the category of rigid analytic varieties as full subcategories. This category has applications in algebraic geometry and rigid analytic geometry. The idea of the definition of the category ~r is the following. From a formal point o...

In the title compound, C26H37N5S, the piperazine ring adopts a chair conformation with the exocyclic N-C bonds in pseudo-equatorial orientations. The piperazine ring (all atoms) subtends dihedral angles of 79.47 (9) and 73.07 (9)° with the triazole and benzene rings, respectively, resulting in an approximate U-shape for the mol-ecule. No significant inter-molecular inter-actions are observed in...