P-Divisible group

Now we apply the Serre-Tate Theorem ([Me] V 2.3) to get a deformation (Y,p) over S of the pair (Yo o) such that the p-divisible group Y[p°°] is isomorphic to the one described above. Finally, after a finite flat base extension such that S is still the spectrum of a complete local ring with residue field we may assume that... 

A p-divisible group scheme or Barsotti-Tate group of corank h is a family of finite abelian group schemes G, of order pf" together with maps i G -> G.+1 such that... 

Demazure, M. Lectures on p-Divisible Groups, Lecture Notes in Math. 302 (New York Springer, 1972). 

Let us take a deformation E of Eq over S = Spec(A [[T]]) such that E is ordinary over the generic point of 5. In this way the polarized p-divisible group yb[p°°] is deformed into... 

Tate, J. p-Divisible Groups, Proceedings of a Conference on Local Fields, Nuffic Summer School at Driebergen, Springer-Verlag, 1967. 

Results of the type obtained here have been previously announced in Cartier s Bourbaki talk [ 7 ]. He assumes the ring Aq is a perfect field of characteristic p and that the Barsotti-Tate groups in question are p-divisible formal Lie groups. Apparently he uses a more "Dieudonne module theoretic" approach. He obtains finer results about the structure of the crystal E)(G) than those obtained here, in particular the result labeled 1) below. 

In either case a) or b) it is immediate that the relevant group is of p-torsion and p-divisible and thus a Barsotti-Tate group. 

Corollary (4.6) If S is artin, a p-divisible formal Lie group is a Barsotti-Tate group with G(l) radiciel and conversely Proof (4. 3) and (4. 5). 

To show G is a Barsotti-Tate group, it must be shown that G is of p-torsion, is p-divisible and that the G(n) are finite and locally-free. 

Serre, J-P. Groupes p-divisibles (d apres J. Tate), Seminaire Bourbaki, expose 318, 1966-67. 

Division of the receptors in the adrenergic nervous system into two classes (a and P) was proposed in 1948 (39) when a difference in the rank order of potency of epinephrine (1, R = CH ), norephinephrine (1, R = H), and isoproterenol [7683-59-2], C H yNO, (1, R = CH(CH3)2) was noted to depend on the organ examined. Eurther subdivision into groups P2 proposed in 1967 (40). Both types of P-adrenoceptors are found throughout the... 

Types of Solids Geldart [Fowder TechnoL, 7, 285-292 (1973)] has characterized four groups of solids that exhibit different properties when fluidized with a gas. Figure 17-j shows the division oi the classes as a function of mean particle size, d,, Im, and densitv difference, (p, — P/ ), g/cm, where p, = particle density and p = fluid density... 

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