Relative Frobenius of plane singularities

Abstract:

In view of the well-known conjecture concerning the classification of lines in the affine plane in characteristic $p > 0$, it is desirable to understand how the characteristic pairs of an irreducible algebroid plane curve are affected by the relative Frobenius. This paper determines the relation between the characteristic sequences $[x,y]$ and $[x,{y^p}]$, where $x$ and $y$ are formal power series in one variable with coefficients in a field of characteristic $p > 0$.