\documentclass[oneside,final,12pt]{book}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{xunicode}

\usepackage{hyperref}
\usepackage{xstring}
\def\rooturl{https://www.math.bgu.ac.il/}
\hyperbaseurl{\rooturl}
\let\hhref\href
\providecommand{\extrahref}[2][]{\LTRfootnote{\LR{\IfBeginWith*{#2}{http}{\nolinkurl{#2}}{\nolinkurl{\rooturl#2}}}}}
\renewcommand{\href}[2]{\IfBeginWith*{#1}{http}{\hhref{#1}{#2}}{\hhref{\rooturl#1}{#2}}\extrahref{#1}}

\usepackage{polyglossia}
\usepackage{longtable}
%% even in English, we sometimes have Hebrew (as in course hours), and we
%% can't add it in :preamble, since it comes after hyperref
%%\usepackage{bidi}
\setdefaultlanguage{hebrew}
\setotherlanguage{english}
%%\setmainfont[Script=Hebrew,Ligatures=TeX]{Libertinus Serif}
\setmainfont[Script=Hebrew,Ligatures=TeX]{LibertinusSerif}[
  UprightFont = *-Regular,
  BoldFont = *-Bold,
  ItalicFont = *-Italic,
  BoldItalicFont = *-BoldItalic,
  Extension = .otf]

%%\newfontfamily{\hebrewfonttt}{Libertinus Serif}
\newfontfamily{\hebrewfonttt}{Liberation Serif}
\SepMark{‭.}
\robustify\hebrewnumeral
\robustify\Hebrewnumeral
\robustify\Hebrewnumeralfinal

% vim: ft=eruby.tex:



\begin{document}
\pagestyle{empty}
\pagenumbering{gobble}

\begin{center}
\vspace*{\baselineskip}

{\Large המחלקה למתמטיקה, בן-גוריון}

\vspace*{\baselineskip}

\rule{\textwidth}{1.6pt}\vspace*{-\baselineskip}\vspace*{2pt}
\rule{\textwidth}{0.4pt}\\[\baselineskip]

{\Huge גאומטריה אלגברית ותורת המספרים}\\[0.2\baselineskip]

\rule{\textwidth}{0.4pt}\vspace*{-\baselineskip}\vspace{3.2pt}
\rule{\textwidth}{1.6pt}\\[\baselineskip]

\textbf{ב}\emph{יום שלישי, 16 ביוני, 2015}
\bigskip

\textbf{בשעה} \emph{10:00 -- 11:00}
\bigskip

\textbf{ב}\emph{Math -101}

\vspace*{2\baselineskip}

ההרצאה

\bigskip
{\Large\bfseries Stability of Gauss valuations\par}
\bigskip

תינתן על-ידי
\bigskip

{\large\scshape Antoine Ducros 
  %
  (Paris 6)
}
\bigskip

\end{center}
\vfill

\textbf{תקציר:}
  \begin{longtable}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
A valued field (k, & . & ) is said to be stable (this terminology has no link with model-theoretic stability theory) if every finite extension L of k is defectless, /i.e. /satisfies the equality ∑ e\_vf\_v= {[}L:k{]} where v goes through the set of extensions of & . & to L, and where e\_v and f\_v are the ramification and inertia indexes of v. The purpose of my talk is to present a new proof (which is part of current joint reflexions with E. Hrushovski and F. Loeser) of the following classical fact (Grauert, Kuhlmann, Temkin\ldots{}) : let (k, & . & ) be a stable valued field, and let (r\_1,\ldots{},r\_n) be elements of an ordered abelian group G containing & k\^{}* & . Let & . & ` be the G-valued valuation on k(T\_1,\ldots{},T\_n) that sends ∑ a\_I T\^{}I to max & a\_I & .r\^{}I. Then (k(T\_1,\ldots{},T\_n), & . & `) is stable too. Our general strategy is purely geometric, but the proof is based upon model-theoretic tools coming from model theory (which I will first present; no knowledge of model theory will be assumed). In particular, it uses in a crucial way a geometric object defined in model-theoretic terms that Hrushovski and Loeser attach to a given k-variety X, which is called its /stable completion/; the only case we will have to consider is that of a curve, in which the stable completion has a very nice model-theoretic property, namely the definability, which makes it very easy to work with.\\
\hline
\end{longtable}
  


\vfill

\bigskip
\begin{center}
{\bfseries אנא שימו לב לשינוי ביום ושעה!}
\end{center}




% vim: ft=eruby.tex:


\end{document}

% vim: ft=eruby.tex:
