\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{english}
\setotherlanguage{hebrew}
%%\setmainfont[Ligatures=TeX]{Libertinus Serif}
\setmainfont[Script=Hebrew,Ligatures=TeX]{LibertinusSerif}[
  UprightFont = *-Regular,
  BoldFont = *-Bold,
  ItalicFont = *-Italic,
  BoldItalicFont = *-BoldItalic,
  Extension = .otf]

\SepMark{‭.}
\robustify\hebrewnumeral
\robustify\Hebrewnumeral
\robustify\Hebrewnumeralfinal

% vim: ft=eruby.tex:



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

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

{\Large Department of Mathematics, BGU}

\vspace*{\baselineskip}

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

{\Huge Jerusalem - Be'er Sheva Algebraic Geometry Seminar}\\[0.2\baselineskip]

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

\textbf{On} \emph{Jan 6, 2021}
\bigskip

\textbf{At} \emph{15:00 -- 16:30}
\bigskip

\textbf{In} \emph{}

\vspace*{2\baselineskip}

{\large\scshape Liran Shaul 
  %
  (Charles University, Prague )
}
\bigskip

will talk about
\bigskip

{\Large\bfseries Derived quotients of Cohen-Macaulay rings\par}
\bigskip

\end{center}
\vfill

\textsc{Abstract:}
It is well known that if A is a Cohen-Macaulay ring and
\$a\_1,\textbackslash{}dots,a\_n\$ is an \$A\$-regular sequence, then the quotient ring
\$A/(a\_1,\textbackslash{}dots,a\_n)\$ is also a Cohen-Macaulay ring. In this talk we
explain that by deriving the quotient operation, if A is a
Cohen-Macaulay ring and \$a\_1,\textbackslash{}dots,a\_n\$ is any sequence of elements in
\$A\$, the derived quotient of \$A\$ with respect to \$(a\_1,\textbackslash{}dots,a\_n)\$ is
Cohen-Macaulay. As an application, we generalize the miracle flatness
theorem to derived algebraic geometry. As another application, given a
morphism \$f:X\textbackslash{}to Y\$ from a Cohen-Macaulay scheme to a nonsingular
scheme, we show that the homotopy fiber of \$f\$ at every point is
Cohen-Macaulay.








% vim: ft=eruby.tex:


\end{document}

% vim: ft=eruby.tex: