T. Sekiguchi and Y. Toda described torsors for the Oort-Tate group  of prime order p under the assumption that prime ideals lying above p in the cyclotomic field are principal. In this paper, we give the Kummer sequence for the cyclotomic twisted tori. We describe torsors for  in the general case. Our method is to consider homomorphisms defining by ideals of the endomorphism ring on a cyclotomic twisted torus.

finite group scheme, torsor, cyclotomic twisted torus.