On the field intersection problem of generic polynomials: a survey

Abstract

Let $k$ be a field of characteristic $\ne 2$. We survey a general method of the field intersection problem of generic polynomials via formal Tschirnhausen transformation. We announce some of our recent results of cubic, quartic and quintic cases the details of which are to appear elsewhere. In this note, we give an explicit answer to the problem in the cases of cubic and dihedral quintic by using multi-resolvent polynomials.

To appear in RIMS Kokyuroku Bessatsu. 17 pages

References in corpus (2)

• On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation
• On the field intersection problem of solvable quintic generic polynomials

Cited by in corpus (1)

• A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations