HACT 2016 Akira Masuoka H

Greenberg ([9, Theorem 4.1]) establishes a relation between the cardinality of Selmer groups of elliptic curves over number fields and the characteristic power series of

The following result about dim X r−1 when p | r is stated without proof, as it follows from the more general Lemma 4.3 in Section 4..

Then we can alter our representation by a suitable multiple of this global 1-cohomology class to make the local representation at G l k+1 special.. It was ramified at the prime

For example, in local class field theory of Kato and Parshin, the Galois group of the maximal abelian extension is described by the Milnor K-group, and the information on

It is not a bad idea but it means that since a differential field automorphism of L|[x 0 ] is given by a birational transformation c 7→ ϕ(c) of the space of initial conditions, we

Byott ([By97a], [By97b], [By99], [By00], [By02]) has constructed examples of wild Galois extensions L|K of local fields with Galois group G where S is not a free module over

Rev. Macmillan Co., New York, N. Uniqueness of Hopf Galois structure for separable field exten- sions. Abelian regular subgroups of the affine group and radical rings.

If the Krull dimension is at least 2, then there are infinitely many prime ideals P of height 1 such that (Λ/P ) is also a formal power series ring, but with Krull dimension reduced