On the field intersection problem of generic polynomials: a survey

Details On the field intersection problem of generic polynomials: a survey On the field intersection problem of generic polynomials: a survey

2008-10-02

arxiv.org/abs/0810.0382v2

Mathematics

Number Theory

To appear in RIMS Kokyuroku Bessatsu. 17 pages

Scientific paper

Let $k$ be a field of characteristic $\neq 2$. 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.

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