IJPAM: Volume 96, No. 4 (2014)
OF PRIME-POWER ORDER
Department of Mathematics
Faculty of Science and Engineering
1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551, JAPAN
Abstract. By the classification theorem by F. Oort and J. Tate [#!o-t!#], any group scheme of prime order is isomorphic to a group scheme under the suitable choice of and . We computed the torsors for some kinds of group schemes in [#!s-t!#], which is a joint work with T. Sekiguchi, as in the following way: denote by a prime number and by the value of the Euler function . Suppose is a prime ideal lying over (which splits completely in ), where is a primitive -st root of the unity. In case is principal, the sequence
is exact, and the Galois descent of is isomorphic to under the suitable choice of and , thus one can compute the torsors for this kinds of group schemes. The non-principal case is solved by Y. Koide [#!koide!#] by using our method. The aim of this paper is to study some group schemes of order a power of a prime number. In section from to , we would like to review the main result of the papers [#!o-t!#] by F. Oort and J. Tate, [#!k-s!#] by Y. Koide and T. Sekiguchi, and [#!s-t!#] by T. Sekiguchi and Y. Toda. In section , we give our main result, namely, the torsor for the Galois descent of .
Received: October 10, 2013
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DOI: 10.12732/ijpam.v96i4.1 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 407 - 425