S. Ishida

activity

20172022

most citedReciprocity law of finite Galois extension fields using Jacobian Varitey

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

math.NT2022

A Note on Tamely Ramified Class Field Theory of Two Dimensional Local Rings

Shinji Ishida

In this note, we treat two dimensional complete local rings which are called "semi-stable local rings" and discuss the tame class filed theory. In 1987, Professor S. Saito complete…

math.NT2021

Principality of prime ideals of algebraic number fields

Shinji Ishida

We discuss principality of prime ideals of finite algebraic number fields $L = K (θ)$ over an algebraic number field $K ([K : Q] < \infty)$ defined by irreducible polynomials $f(…

math.GM2020★ 1 cited

Reciprocity law of finite Galois extension fields using Jacobian Varitey

Shinji Ishida

For finite Galois extension fields defined by odd degree irreducible polynomials over algebraic integer ring, we observe "Reciprocity Law" through Jacobian Variety by embedding all…

math.NT2017

An Approach to Non-Abelian Cyclotomic Fields

Shinji Ishida

We mainly study a polynomial $f_{1, n} (x) = x^{n - 1} + 2 x^{n - 2} + 3 x^{n - 3} + \dots + k x^{n - k} + \dots + (n - 1) x + n$ over $Z$ and the Galois group of the minimal splitting fi…