Ofer Gabber, Adrian Vasiu. Dimensions of group schemes of automorphisms of truncated Barsotti-tate groups

Natural Sciences / Mathematics / Number theory

Submitted on: Aug 18, 2012, 20:04:54

Description: Let D be a p-divisible group over an algebraically closed field k of characteristic p>0. Let n_D be the smallest non-negative integer such that D is determined by D[p^{n_D}] within the class of p-divisible groups over k of the same codimension c and dimension d as D. We study n_D, lifts of D[p^m] to truncated Barsotti--Tate groups of level m+1 over k, and the numbers $gamma_D(i):=dim(pmb{Aut}(D[p^i]))$. We show that $n_Dle cd$, $(gamma_D(i+1)-gamma_D(i))_{iinBbb N}$ is a decreasing sequence in $Bbb N$, for $cd>0$ we have $gamma_D(1) The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.