Ramification groups of Galois extensions over local fields of positive characteristic with Galois group isomorphic to the group of unitriangular matrices
Acta Arithmetica
MSC: Primary 11S15; Secondary 12F10
DOI: 10.4064/aa251129-19-6
Opublikowany online: 25 August 2026
Streszczenie
We study the ramification groups of finite Galois extensions $L/K$ of a complete discrete valuation field $K$ of equal characteristic $p \gt 0$ with perfect residue field and Galois group isomorphic to the group of unitriangular matrices $UT_n(\mathbb {F}_p)$ over $\mathbb {F}_p$. We show that the upper ramification breaks can be expressed as a linear function of the valuation of the entries of a matrix directly constructed from the coefficients of a defining equation of the extension. This allows us to compute the ramification groups without using any elements of $L-K$.
