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...

Forey, Arthur
Published in
Selecta Mathematica

Let k be a field of characteristic zero containing all roots of unity and K=k((t))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K=k(( t))$$\end{document}. We build a ...

Sasaki, Shu
Published in
Inventiones mathematicae

We prove the strong Artin conjecture for continuous, totally odd, two-dimensional representations of the absolute Galois group of a totally real field F.

津嶋, 貴弘

"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. / In this survey article, we explain the contents of [Sch, §1-§7]. Our main aim is to introduce the definition of perfecto...

伊藤, 哲史

"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. / We give a brief survey on number theoretic applications of the theory of perfectoid spaces recently obtained by Peter Sc...

Ludwig, Judith
Published in
manuscripta mathematica

We prove a p-adic Labesse–Langlands transfer from the group of units in a definite quaternion algebra to its subgroup of norm one elements. More precisely, given an eigenvariety for the first group, we show that there exists an eigenvariety for the second group and a morphism between them that extends the classical Langlands transfer. In order to f...

Remy, Bertrand Thuillier, Amaury Werner, Annette

Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equivariantly identified with the compactification which we get by embedding the building in the Berkovich analytic space associated to the wonderful compactification of the gr...

Thuong, Lê Quy
Published in
Acta Mathematica Vietnamica

In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these invariants. A purpose of this note is to show how the conjecture arises. Because of the integral identity’s nature, we shall give a...

Obus, Andrew Wewers, Stefan
Published in
Research in the Mathematical Sciences

Given a branched cover f:Y→X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f{:}\,Y\rightarrow X$$\end{document} between smooth projective curves over a non-archimedean...

Draisma, Jan Postinghel, Elisa
Published in
Manuscripta Mathematica

For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a r...