Potentially Good Reduction of Barsotti-Tate Groups

Details Potentially Good Reduction of Barsotti-Tate Groups Potentially Good Reduction of Barsotti-Tate Groups

2006-04-27

arxiv.org/abs/math/0604593v1

Mathematics

Number Theory

Scientific paper

Let R be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a finite extension K' of K. We prove that there exists a constant c which depends on the absolute ramification index e(K'/Q_p) and the height of G such that G has good reduction over K if and only if G[p^c] can be extended to a finite flat group scheme over R. For abelian varieties with potentially good reduction, this result generalizes Grothendieck's p-adic Neron-Ogg-Shafarevich criterion to finite level. We use methods that can be generalized to study semi-stable p-adic Galois representations with general Hodge-Tate weights, and in particular leads to a proof of a conjecture of Fontaine and gives a constant c as above that is independent of the height of G.

Affiliated with

Also associated with

No associations

Rating

Potentially Good Reduction of Barsotti-Tate Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Potentially Good Reduction of Barsotti-Tate Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Potentially Good Reduction of Barsotti-Tate Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-20987