Groupes p-Divisibles, Groupes Finis et Modules Filtres

Canonicalq-deformations in arithmetic geometry

“…(6) We note that this is clear after the choice of coordinates; the conjecture says that the isomorphism commutes with coordinate transformations. Using the comparison between étale and singular cohomology, the next theorem states that Conjecture 3.3 holds true in this context: …”

“…In abstract p-adic Hodge theory, the q-de Rham complex is closely related to the theory of Wach modules, [3,25], which only works for abelian extensions of Q p . For general extensions of Q p , there is the theory of Breuil-Kisin modules, [6,16], which depends on a choice of uniformizer of K. One might expect that there is a Breuil-Kisin variant of the q-de Rham complex; however, this seems harder to write down explicitly, as the variable q is tied with the roots of unity. One may also wonder about Lubin-Tate variants.…”

The correspondence between Barsotti-Tate groups and Kisin modules when p=2

“…(1) is Proposition 5.1.3 of [3]. Note that proof of the proposition does not need the running assumptions of the paper: p > 2 and k is finite.…”

Mathematisches Institut Georg-August-Universität Göttingen Seminars Winter Term 2004/2005

“…The goal of this paper is the study of FGS O L and of Abelian varieties over L. We note that a certain classification of FGS O L for L being perfect was given by Breuil (see [Bre00]); yet that classification is inconvenient for several types of problems.…”