A ramification filtration of the Galois group of a local field. (English) Zbl 0873.11063

Ladyzhenskaya, O. A. (ed.), Proceedings of the St. Petersburg Mathematical Society. Vol. III. Transl. ed. by A. B. Sosinsky. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 166, 35-100 (1995).
Let \(K\) be a local field of characteristic \(p\) with residue class field \(k= \overline \mathbb{F}_p\). Let \(\Gamma\) be the Galois group of a separable algebraic closure \(\overline K\) of \(K\) and let \(I\) be the subgroup corresponding to the maximal tamely ramified extension. The author gives a description of the group \(\Gamma/I^p C_p(I)\), where \(C_p(I)\) is the closed subgroup of \(I\) generated by the commutators of order \(p\), together with the higher ramification group of \(\Gamma/I^p C_p(I)\). This description is based on a generalized theory of Artin-Schreier extensions by means of filtered associative bialgebras, which is of interest of its own. The final result is too complicated to be described in this review. The referee recommends the reader to fight his way through this rather long but important paper.
For the entire collection see [Zbl 0822.00006].
Reviewer: H.Koch (Berlin)


11S15 Ramification and extension theory
11S20 Galois theory