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...

Besser, Amnon de Shalit, Ehud
Published in
Annales mathématiques du Québec

We construct two types of L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {L}}$$\end{document}-invariants attached to varieties which are uniformized by Drin...

Ulirsch, Martin
Published in
Mathematische Zeitschrift

In this article we define a natural tropicalization procedure for closed subsets of log-regular varieties in the case of constant coefficients and study its basic properties. This framework allows us to generalize some of Tevelev’s results on tropical compactification as well as Hacking’s result on the cohomology of the link of a tropical variety t...

Imai, Naoki Tsushima, Takahiro

"Algebraic Number Theory and Related Topics 2012". December 3～7, 2012. edited by Atsushi Shiho, Tadashi Ochiai and Noriyuki Otsubo. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / In this paper, we construct semi-stable models of Lubin-Tate curves with level one or two, and determine their reductions...

Cornelissen, Gunther Kato, Fumiharu Kool, Janne
Published in
Mathematische Annalen

We present a method to control gonality of nonarchimedean curves based on graph theory. Let k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document} denote a ...

Shen, Xu
Published in
Mathematische Annalen

In this paper we study the p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adic analytic geometry of the basic unitary group Rapoport–Zink spaces MK\...

Peng, Fan
Published in
Science China Mathematics

Let f: X → U be a family of smooth hypersurfaces in ℙn of degree d > n+1 over a smooth curve U. Assume that the Griffiths-Yukawa coupling of f is non-vanishing. Then f is rigid. Moreover, we generalize it to the case when the Griffiths-Yukawa coupling of f is degenerated.

Cueto, Maria Angelica Häbich, Mathias Werner, Annette
Published in
Mathematische Annalen

We show that the tropical projective Grassmannian of planes is homeomorphic to a closed subset of the analytic Grassmannian in Berkovich’s sense by constructing a continuous section to the tropicalization map. Our main tool is an explicit description of the algebraic coordinate rings of the toric strata of the Grassmannian. We determine the fibers ...

Saito, Takeshi
Published in
Acta Mathematica Vietnamica

The monodromy weight conjecture is one of the main remaining open problems on Galois representations. It implies that the local Galois action on the ℓ-adic cohomology of a proper smooth variety is almost completely determined by the traces. Peter Scholze proved the conjecture in many cases including smooth complete intersections in a projective spa...