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\section*{Alexander Grothendieck}

The European mathematician \textbf{Alexander Grothendieck} (in French sometimes Alexandre Grothendieck), created a very influential body of work foundational for ([[algebraic geometry|algebraic]]) [[geometry]] but also for modern [[mathematics]] more generally. He is widely regarded as a singularly important figure of 20th century mathematics and his ideas continue to be highly influential in the 21st century.

\begin{itemize}%
\item \href{http://en.wikipedia.org/wiki/Alexander_Grothendieck}{Wikipedia article}

\end{itemize}
Initially working on [[topological vector spaces]] and [[analysis]], Grothendieck then made revolutionary advances in [[algebraic geometry]] by developing [[sheaf and topos theory]] and [[abelian sheaf cohomology]] and formulating algebraic geometry in these terms ([[locally ringed spaces]], [[schemes]]). Later [[topos theory]] further developed independently and today serves as the foundation also for other kinds of [[geometry]]. Notably its [[homotopy theory|homotopy theoretic]] refinement to [[higher topos theory]] serves as the foundation for modern [[derived algebraic geometry]].

\hypertarget{texts_by_grothendieck}{}\subsection*{{Texts by Grothendieck}}\label{texts_by_grothendieck}

Grothendieck's geometric work is documented in texts known as [[EGA]] (with [[Dieudonné]]), an early account [[FGA]], and the many volume account [[SGA]] of the seminars at l'IH\'E{}S, Bures-sur-Yvette, where he was based at the time. (See the \href{http://en.wikipedia.org/wiki/Alexander_Grothendieck}{wikipedia article} for some indication of the story from there until the early 1980s.)

In the late 1970s and early 1980s Grothendieck wrote several documents that have been of outstanding importance in the origins of the theory that underlies the [[nPOV]]. These include

\begin{itemize}%
\item \emph{La Longue Marche \`a{} travers la Th\'e{}orie de Galois} (1600 manuscript pages written between January and June 1981, plus addenda etc. which double its length!) (see [[Long March]] for some discussion of the ideas.)


\item \emph{[[Esquisse d'un programme]]}, (January 1984), in which Grothendieck sketches out a vaste programme of research, incorporating many of the ideas from [[Long March]]. A copy is available \href{http://www.math.jussieu.fr/~leila/grothendieckcircle/EsquisseFr.pdf}{here}. It is discussed in brief at [[Esquisse d'un programme|Grothendieck's Esquisse]].


\item \emph{\`A{} la poursuite des Champs} (also entitled `'[[Pursuing Stacks]]'').\newline It starts with a short (12 page) letter to Quillen, dated 19 Feb. 1983, but then discusses a wide ranging vision of homotopy theory and its applicability to problems in algebraic and arithmetic geometry.


\item \emph{[[Les Dérivateurs]]} (another 2000 page manuscript taking up some of the themes in Pursuing Stacks, section 69) Dating from the end of 1990 and the start of 1991.



\end{itemize}
In the same time he also wrote voluminous intellectual memoirs \emph{Recoltes et Semailles}.

En Guise de Programme \href{https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Guise1.jpg}{p I} \href{https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Guise2.jpg}{p II}, a text written by Grothendieck as a course description while teaching in Montpellier ``Introduction \`a{} la recherche''.

A chronological bibliography of Grothendieck's published mathematical writings (\href{https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/GrothBiblio.pdf}{pdf}).

\hypertarget{texts_about_grothendieck}{}\subsection*{{Texts about Grothendieck}}\label{texts_about_grothendieck}

For an account of his work, including some of the work published in the 1980s, see the \href{http://en.wikipedia.org/wiki/Alexander_Grothendieck}{English Wikipedia entry}.

The video of a talk by W. Scharlau on his life can be seen \href{http://www.dailymotion.com/video/x8juek_colloque-grothendieck-winfried-scha_tech}{here}.

\begin{itemize}%
\item Reminiscenes of Grothendieck, 2007 conversations of [[Sasha Beilinson]], [[Luc Illusie]], [[Vladimir Drinfel'd]], [[Spencer Bloch]], (\href{http://www.math.uchicago.edu/~mitya/langlands/reminiscences1.pdf}{pdf})


\item [[Pierre Cartier]], \emph{Alexander Grothendieck: A Country Known Only by Name} (\href{http://www.ams.org/notices/201504/rnoti-p373.pdf}{pdf})


\item [[Luca Barbieri-Viale]], \emph{Alexander Grothendieck: Enthusiasm and creativity} (\href{https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Mathbiographies/barbierieng.pdf}{pdf})


\item [[Pierre Deligne]], \emph{Quelques id\'e{}es ma\^i{}tresses de l'\oe{}uvre de A Grothendieck} (\href{http://www.math.jussieu.fr/~leila/grothendieckcircle/Mathbiographies/Deligne.pdf}{pdf})


\item [[Luc Illusie]], \emph{Alexandre Grothendieck, le magicien des foncteurs} (\href{http://www.cnrs.fr/insmi/IMG/pdf/Alexandre-Grothendieck.pdf}{pdf})


\item \emph{Une entrevue avec [[Jean Giraud]], \`a{} propos d'Alexandre Grothendieck} (\href{https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/giraud.pdf}{pdf}).



\end{itemize}
A recent article in French on Grothendieck is to be found \href{http://images.math.cnrs.fr/Alexandre-Grothendieck.html}{here}.

There were two articles on Grothendieck's life and work in the Notices AMS in 2004:

\begin{itemize}%
\item Allyn Jackson, \emph{Comme Appel\'e{} du N\'e{}ant}, As If Summoned from the Void: The Life of Alexandre Grothendieck, Part 1, \href{http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf}{Notices AMS}


\item Allyn Jackson, \emph{Comme Appel\'e{} du N\'e{}ant}, As If Summoned from the Void: The Life of Alexandre Grothendieck, Part 2, \href{http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf}{Notices AMS}



\end{itemize}
Grothendieck obituary in the Notices AMS (Michael Artin, Allyn Jackson, David Mumford, and John Tate, Coordinating Editors):

\begin{itemize}%
\item ``\emph{The obituary begins here with a brief sketch of Grothendieck's life, followed by a description of some of his most outstanding work in mathematics.}'' Alexandre Grothendieck 1928--2014, (\href{http://www.ams.org/journals/notices/201603/rnoti-p242.pdf}{Part 1})


\item ``\emph{set of reminiscences by some of the many mathematicians who knew Grothendieck and were influenced by him.}'' Alexandre Grothendieck 1928--2014, (\href{http://www.ams.org/publications/journals/notices/201604/rnoti-p401.pdf}{Part 2}).



\end{itemize}
\hypertarget{students}{}\subsection*{{Students}}\label{students}

\begin{itemize}%
\item [[Pierre Gabriel]]
\item [[Michel Demazure]]
\item [[Jean Giraud]]
\item [[Jean-Louis Verdier]]
\item [[Monique Hakim]]
\item [[Michel Raynaud]]
\item [[Jean-Pierre Jouanolou]]
\item [[Luc Illusie]]
\item [[William Messing]]
\item [[Pierre Berthelot]]
\item [[Pierre Deligne]]
\item [[Michèle Raynaud]]
\item [[Neantro Saavedra-Rivano]]
\item [[Hamet Seydi]]
\item [[Hoàng Xuân Sính]]
\item [[Yves Ladegaillerie]]
\item [[Marcus Wanderley]]
\item [[Carlos Contou-Carrère]]

\end{itemize}
See \emph{\href{http://www.genealogy.ams.org/id.php?id=31245}{Mathematics Genealogy for Grothendieck}}

\hypertarget{correspondence}{}\subsection*{{Correspondence}}\label{correspondence}

\href{http://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Letters/GS.pdf}{The Grothendieck-Serre correspondence}

\href{http://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Letters/AGMumford.pdf}{The Grothendieck-Mumford correspondence}

\hypertarget{external_links}{}\subsection*{{External links}}\label{external_links}

\href{http://www.grothendieckcircle.org/}{Grothendieck circle}

\href{https://www.dropbox.com/s/9u7n6xkwytocogf/grothendieckangle.pdf?dl=0}{Grothendieck's Angle} by G. Aiello

\href{http://matematicas.unex.es/~navarro/res/}{A. Grothendieck} by J. A. Navarro

\href{https://agrothendieck.github.io/}{A. Grothendieck} by M. Carmona

A. Grothendieck, una guía a la obra matemática y filosófica (\href{http://matematicas.unex.es/~navarro/res/zalamea.pdf}{pdf}) por F. Zalamea

category: people

[[!redirects Grothendieck]] [[!redirects A. Grothendieck]] [[!redirects Alexander Grothendieck]] [[!redirects Alexandre Grothendieck]]



\end{document}