Program to enhance tae transfer of new technology to potential industrial, governmental, and academic users in the oklahoma area Quarterly status report, 1 Jul. - 30 Sep. 1967

Aerospace technology applications to industr

Construction of a profile of the existing economic structure of the region surrounding the Southeastern State College. Program to enhance the transfer of new technology to potential industrial, governmental Quarterly status report, 1 Jan. - 31 Mar.

Technology utilization program for use in regional economic profil

Purity results for pp-divisible groups and abelian schemes over regular bases of mixed characteristic

Let $p$ be a prime. Let (R,\ideal{m}) be a regular local ring of mixed characteristic $(0,p)$ and absolute index of ramification $e$. We provide general criteria of when each abelian scheme over \Spec R\setminus\{\ideal{m}\} extends to an abelian scheme over \Spec R. We show that such extensions always exist if $e\le p-1$, exist in most cases if $p\le e\le 2p-3$, and do not exist in general if $e\ge 2p-2$. The case $e\le p-1$ implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring $O$ of mixed characteristic $(0,p)$ and index of ramification at most $p-1$. This leads to large classes of examples of N\'eron models over $O$. If $p>2$ and index $p-1$, the examples are new.Comment: 28 pages. Final version identical (modulo style) to the galley proofs. To appear in Doc. Mat

Families of p-divisible groups with constant Newton polygon

A p-divisible group over a base scheme in characteristic p in general does not admit a slope filtration. Let X be a p-divisible group with constant Newton polygon over a normal noetherian scheme S; we prove that there exists an isogeny from X to Y such that Y admits a slope filtration. In case S is regular this was proved by N. Katz for dim(S) = 1 and by T. Zink for dim(S) > 0. We give an example of a p-divisible group over a non-normal base which does not admit an isogeny to a p-divisible group with a slope filtration.Comment: To be published in Documenta Mathematic

On the Drinfeld moduli problem of p-divisible groups

Let $O_D$ be the ring of integers in a division algebra of invariant $1/n$ over a p-adic local field. Drinfeld proved that the moduli problem of special formal $O_D$-modules is representable by Deligne's formal scheme version of the Drinfeld p-adic halfspace. In this paper we exhibit other moduli spaces of formal $p$-divisible groups which are represented by $p$-adic formal schemes whose generic fibers are isomorphic to the Drinfeld p-adic halfspace. We also prove an analogue concerning the Lubin-Tate moduli space.Comment: Expanded introductio