Fadil, Lhoussain El
Published in
Mathematica Slovaca

In this paper, we develop a new method based on Newton polygon and graded polynomials, similar to the known one based on Newton polygon and residual polynomials. This new method allows us the factorization of any monic polynomial in any henselian valued field. As applications, we give a new proof of Hensel’s lemma and a theorem on prime ideal facto...

Bojković, Velibor Poineau, Jérôme
Published in
Mathematische Annalen

Let k be a complete nontrivially valued non-archimedean field. Given a finite morphism of quasi-smooth k-analytic curves that admit finite triangulations, we provide upper bounds for the number of connected components of the ramification locus in terms of topological invariants of the source curve such as its topological genus, the number of points...

TAKATA, Megumi

"Algebraic Number Theory and Related Topics 2015". November 30 - December 4, 2015. edited by Hiroki Takahashi, Yasuo Ohno and Takahiro Tsushima. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / In this paper, we construct a base change lifting for an APF extension of a mixed characteristic local field...

Hu, Haoyu

"Algebraic Number Theory and Related Topics 2015". November 30 - December 4, 2015. edited by Hiroki Takahashi, Yasuo Ohno and Takahiro Tsushima. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / This is an announcement of the joint article [HY] with E. Yang, based on a talk given in December 2015 at RI...

Shimomoto, Kazuma
Published in
Mathematische Annalen

The main result of this article is to prove that any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen–Macaulay algebra. The proof of this result is based on the construction of almost Cohen–Macaulay algebras in mixed characteristic due to Yves André. Moreover, we prove that the absolute integral closure of a ...

Cutkosky, Steven Dale
Published in
Acta Mathematica Vietnamica

We show that if R is a local domain which is dominated by a valuation ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\nu $\end{document}, then there does not always ex...

Checcoli, Sara
Published in
manuscripta mathematica

In this paper, we consider infinite Galois extensions of number fields and study the relation between their local degrees and the structure of their Galois groups. It is known that, if K is a number field and L / K is an infinite Galois extension of group G, then the local degrees of L are uniformly bounded at all rational primes if and only if G h...

Dummit, David S. Kisilevsky, Hershy
Published in
Research in Number Theory

We examine whether it is possible to realize finite groups G as Galois groups of minimally tamely ramified extensions of Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}...

Yatagawa, Yuri

"Algebraic Number Theory and Related Topics 2014". December 1～5, 2014. edited by Takeshi Tsuji, Hiroki Takahashi and Yuichiro Hoshi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / This is a research announcement about a study of characteristic cycle of a rank 1 sheaf on a surface on which I am writi...

Pati, Maria Rosaria
Published in
Annales mathématiques du Québec

Let K be a p-adic field. Restricting to the case of no intermediate extensions, we obtain formulæ counting the number of (totally and wildly) ramified extensions of degree p4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek...