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

In the title compound, C21H22N2O, the planes of the two six-membered rings make a dihedral angle of 89.51 (7)°. The pyrrolidine ring has a puckering amplitude q 2 = 0.418 (3) and a pseudo-rotation phase angle ϕ2 = -166.8 (5), adopting a twist conformation (T). The other five-membered ring has a puckering amplitude q 2 = 0.247 (2) and a pseudo-rotation phase angle ϕ2 = -173.7 (5), adopting an en...

The title compound, C15H14N2OS2, adopts a helix conformation. An intra-molecular N-H⋯O hydrogen bond leads to a six-membered pseudo-ring [r.m.s. deviation = 0.0212 Å, maximum deviation = 0.033 (1) Å for the N atom bearing the benzoyl group] in the central unit. The benzene and (methyl-sulfan-yl)benzene ring [r.m.s = 0.0028 Å and largest deviation of 0.067 (3) Å for the methyl-sulfanyl C atom] m...

The title compound, C23H21ClN4, contains two molecules (A and B) in the asymmetric unit, which are related to one another by a pseudo-inversion center. The non-aromatic pyrrolidine ring in each independent mol-ecule adopts a half-chair conformation; the ring puckering parameters are θ = 0.407 (3) Å and ϕ = 270.5 (4)°, and the pseudo-rotation parameters are ρ = 72.5 (3)° and τ = 42.2 (2)° for an...

We prove, for an arithmetic scheme X/S over a discrete valuation ring whose special fiber is a strict normal crossings divisor in X, that the Swan conductor of X/S is equal to the Euler characteristic of the torsion in the logarithmic de Rham complex of X/S. This is a precise logarithmic analog of a theorem by Bloch [1].

Contents Introduction 2 1. Homology theory, cycle map, and Kato complex 6 2. Vanishing theorem 10 3. Bertini theorem over a discrete valuation ring 14 4. Surjectivity of cycle map 17 5. Blowup formula and moving lemma 19 6. Proof of main theorem 21 7. Applications of main theorem 23 References 25 1 2 SHUJI SAITO AND KANETOMO SATO

We show that the algebraic K -theory of generalized archimedean valuation rings occurring in Durov’s compactification of the spectrum of a number ring is given by stable homotopy groups of certain classifying spaces.We also show that the “residue field at infinity” is badly behaved from a K -theoretic point of view.

Contents Introduction 2 1. Homology theory and cycle map 6 2. Kato homology 12 3. Vanishing theorem 16 4. Bertini theorem over a discrete valuation ring 20 5. Surjectivity of cycle map 23 6. Blow-up formula 25 7. A moving lemma 28 8. Proof of main theorem 30 9. Applications of main theorem 33 Appendix A.

We give axiomatizations and quantifier eliminations for first-order theories of finitely ramified valued fields with an automorphism having a close interaction with the valuation. We achieve an analogue of the classical Ostrowski theory of pseudoconvergence. In the outstanding case of Witt vectors with their Frobenius map, we use the ∂-ring formalism from Joyal.

We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.