Universal Extensions and One Dimensional Crystalline Cohomology

  title={Universal Extensions and One Dimensional Crystalline Cohomology},
  author={Barry Mazur and William Messing},

Universal extension crystals of 1-motives and applications

Introduction to Shimura Varieties with Bad Reduction of Parahoric Type

This survey article explains the construction of Rapoport-Zink local models and their use in understanding various questions relating to the singularities in the reduction modulo p of certain Shimura

Formal sections and de Rham cohomology of semistable Abelian varieties

We give a geometric description of the unit root splitting of the Hodge filtration of the first de Rham cohomology of an ordinary Abelian variety over a local field, as the splitting determined by a

Compactifications of splitting models of PEL-type Shimura varieties

We construct toroidal and minimal compactifications, with expected properties concerning stratifications and formal local structures, for all integral models of PEL-type Shimura varieties defined by

Vectorial extensions of Jacobians

In this paper, we make explicit the connection between the theory of the universal vectorial extension as developed in Universal Extensions and One Dimensional Crystalline Cohomology [MaMe] and the

Crystalline representations and F -crystals

Following ideas of Berger and Breuil, we give a new classification of crystalline representations. The objects involved may be viewed as local, characteristic 0 analogues of the “shtukas” introduced

Crystalline realizations of 1-motives

Abstract.We consider the crystalline realization of Deligne’s 1-motives in positive characteristics and prove a comparison theorem with the De Rham realization of (formal) liftings to zero

Deligne's conjecture on 1-motives

We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soule on cohomology, and prove it. This implies the original conjecture up to isogeny. If the

The universal vector extension of an abeloid variety

. Let A be an abelian variety over a complete non-Archimedean field K . The universal cover of the Berkovich space attached to A reflects the reduction behaviour of A . In this paper the universal

Additive extensions of a Barsotti-Tate group

In this paper we classify up to isomorphism the additive extensions of a Barsotti-Tate group, in positive characteristic p over a perfect field k and in characteristic 0 over W(k) the ring of Witt