Barsotti–Tate group
In algebraic geometry, Barsotti–Tate groups or "p"-divisible groups are similar to the points of order a power of "p" on an abelian variety in characteristic "p". They were introduced by under the name equidimensional hyperdomain and by under the name p-divisible groups, and named Barsotti–Tate groups by . Definition. defined a "p"-divisible group of height "h" (over a scheme "S") to be an inductive system of groups "G" for "n"≥0, such that "G" is a finite group scheme over "S" of order "p" and such that "G" is (identified with) the group of elements of  order divisible by "p" in "G". More generally, defined a Barsotti–Tate group "G" over a scheme "S" to be an fppf sheaf of commutative groups over "S" that is "p"-divisible, "p"-torsion, such that the points "G"(1) of order "p" of "G" are (represented by) a finite locally free scheme. The group "G"(1) has rank "p" for some locally constant function "h" on "S", called the rank or height of the group "G". The subgroup "G"("n") of points of order "p" is a scheme of rank "p", and "G" is the direct limit of these subgroups. Barsotti–Tate group In