We give two algorithms to compute linear determinantal representations of
smooth plane curves of any degree over any field. As particular examples, we
explicitly give representatives of all equivalence classes of linear
determinantal representatio...

In this article, we study the monoid of fractional ideals and the ideal class
semigroup of an arbitrary given one dimensional normal domain O obtained by an
infinite integral extension of a Dedekind domain. We introduce a notion of
"upper semicont...

Let T be a free Z_p-module of finite rank equipped with a continuous
Z_p-linear action of the absolute Galois group of a number field K satisfying
certain conditions. In this article, by using a Selmer group corresponding to
T, we give a lower bou...

We use explicit methods to study the 4-torsion points on the Jacobian variety
of the Fermat quartic. With the aid of computer algebra systems, we explicitly
give a basis of the group of 4-torsion points. We calculate the Galois action,
and show th...

In this article, we study the pseudo-isomorphism class of the dual fine
Selmer group attached to a -adic Galois deformation whose deformation
ring is isomorphic to the ring of formal power series. By using the
"Kolyvagin system" a...

In our previous work, by using Kolyvagin derivatives of elliptic units, we
constructed ideals C_i of the Iwasawa algebra, and proved that the ideals C_i
become "upper bounds" of the higher Fitting ideals of the one and two variable
p-adic unramifi...