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\begin{document}

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\section*{FGA explained}

One of the series of Grothendieck's works is FGA (see entry [[EGA]] for overall description of EGA, FGA and SGA). A summer school in Trieste 2003, has tried to summarize some of the main historical breakthroughs of FGA in modern exposition. The proceedings of that school are an updated version of freely available materials on the ICTP web.

\begin{itemize}%
\item Barbara Fantechi, Lothar G\"o{}ttsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure, Angelo Vistoli, \emph{Fundamental algebraic geometry. Grothendieck's FGA explained}, Mathematical Surveys and Monographs \textbf{123}, Amer. Math. Soc. 2005. x+339 pp. \href{http://www.ams.org/mathscinet-getitem?mr=2007f:14001}{MR2007f:14001}

\end{itemize}
\hypertarget{contents}{}\subsubsection*{{Contents}}\label{contents}

\begin{itemize}%
\item [[Angelo Vistoli]], Grothendieck topologies, fibered categories and descent theory (1--104) \href{http://www.ams.org/mathscinet-getitem?mr=2223406}{MR2223406}; \href{http://arxiv.org/abs/math/0412512}{math.AG/0412512}.


\item Nitin Nitsure, Construction of Hilbert and [[Quot scheme]]s (105--137) \href{http://www.ams.org/mathscinet-getitem?mr=2223407}{MR2223407}; \href{https://arxiv.org/abs/math/0504590}{math/0504590}


\item Barbara Fantechi and Lothar G\"o{}ttsche, Local properties and Hilbert schemes of points (139--178) MR2223408; (draft \href{http://cdsagenda5.ictp.it//askArchive.php?categ=a0255&id=a0255s7t5&ifd=13843&down=1&type=lecture_notes}{pdf})


\item Luc Illusie, [[Grothendieck's existence theorem]] in formal geometry (179--233) MR2223409; (draft version \href{http://cdsagenda5.ictp.it//askArchive.php?categ=a0255&id=a0255s3t3&ifd=15021&down=1&type=lecture_notes}{pdf})


\item [[Steven Kleiman|Steven L. Kleiman]], The Picard scheme (235--321) MR2223410 (draft \href{http://cdsagenda5.ictp.it//askArchive.php?categ=a0255&id=a0255s6t3&ifd=15022&down=1&type=lecture_notes}{pdf})



\end{itemize}
See the \href{http://indico.ictp.it/event/a0255/other-view?view=ictptimetable}{conference page} for scans of the lecture notes.



\end{document}