Tame-blind Extension of Morphisms of Truncated Barsotti-tate Group Schemes

The purpose of the present paper is to show that morphisms between the generic fibers of truncated Barsotti-Tate group schemes over mixed characteristic complete discrete valuation rings with perfect residue fields extend in a “tame-blind” fashion — i.e., under a condition which is unaffected by passing to a tame extension — to morphisms between the original truncated Barsotti-Tate group schemes. The “tame-blindness” of our extension result allows one to verify the analogue of a result of Tate for isogenies of Barsotti-Tate groups over the ring of integers of the p-adic completion of the maximal tamely ramified extension field.