We calculate the number of extensions of Raynaud schemes over the ring of integers of an absolutely ramified p-adic field with the trivial generic fibers by counting the rational points of the moduli space of finite flat models. Introduction Let K be a totally ramified extension of degree e over Qp for p > 2, and F be a finite field of characteristic p. We consider the constant group scheme CF ...

Let M be a complete nonsingular fine moduli space of modules over an algebra S. A set of conditions is given for the Chow ring of M to be generated by the Chern classes of certain universal bundles occurring in a projective resolution of the universal S-module on M . This result is then applied to the varieties GT parametrizing homogeneous ideals of k[x, y] of Hilbert function T , to moduli spa...

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor D-modules. As an application, we show the hard Lefschetz theorem for algebraic semisimple holonomic D-modules, conjectured by M. Kashiwara. We also study resolutio...

In the case of local fields of positive characteristic we introduce an analogue of Fontaine’s concept of Galois modules with crystalline height h ∈ N. If h = 1 these modules appear as geometric points of Faltings’s strict modules. We obtain upper estimates for the largest upper ramification numbers of these modules and prove (under an additional assumption) that these estimates are sharp. 0. In...

Since Eilenberg and Moore [EM], the relative homological algebra, especially the Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The analogues for the basic notion, such as projective, injective, flat, and free modules, are respectively the Gorenstein projective, the Gorenstein injective, the Gorenstein flat, and the strongly Gorenstein projective modules. One c...

Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was recently introduced by Faltings and appears as an equal characteristic analogue of the classical category of finite flat group schemes. In this paper we obtain a classification of these modules and apply it to prove analogues of properties, which ...

Let $R$ be a ring, $S$ multiplicative subset of $R$. An $R$-module $M$ is said to $u$-$S$-flat ($u$- always abbreviates uniformly) if $\Tor^R_1 (M, N)$ $u$-$S$-torsion for all $R$-modules $N$. In this paper, we introduce and study the concept $S$-cotorsion module which in some way generalization notion cotorsion module. $\Ext^1_R(F,M)=0$ any $F$. This new class modules will used characterize $u...