Editing Pierre Cartier (mathematician)

{{Short description|French mathematician (1932–2024)}}
{{Infobox scientist
| name              = Pierre Cartier
| image             = Pierre Cartier 2009.jpg
| image_size        = 
| caption           = Cartier in 2009
| birth_name        = Pierre Émile Cartier
| birth_date        = {{birth date|1932|06|10|df=y}}
| birth_place       = [[Sedan, Ardennes|Sedan]], [[French Third Republic|France]]
| death_date        = {{death date and age|2024|08|17|1932|06|10|df=y}}
| death_place       = [[Marcoussis]], France
| fields            = [[Mathematics]]
| workplaces        = [[University of Strasbourg]]<br>[[Institut des Hautes Études Scientifiques]]
| education         = [[Lycée Saint-Louis]]
| alma_mater        = [[École normale supérieure (Paris)|École normale supérieure]]<br>[[University of Paris]]
| doctoral_advisor  = [[Henri Cartan]]<br>[[André Weil]]
| doctoral_students = [[Guy Henniart]]
| known_for         = [[Cartier divisor]]<br>[[Cartier duality]]<br>[[Cartier isomorphism]]<br>[[Hasse–Witt_matrix#Cohomology|Cartier operator]]<br>[[Distribution on a linear algebraic group|Cartier's theorem]]<br>[[Manin_matrix#Properties|Cartier–Foata matrices]]<br>[[Trace monoid|Traces]]
| awards            = [[Prix Peccot]] (1960)<ref>{{cite web|title=Pierre Cartier|website=Institute for Advanced Study|date=9 December 2019 |url=https://www.ias.edu/scholars/pierre-cartier}}</ref><br>[[List of International Congresses of Mathematicians Plenary and Invited Speakers|ICM Speaker]] (1970)<br>[[Prize Ampère]] (1978)
}}

'''Pierre Émile Cartier''' (10 June 1932 – 17 August 2024) was a French mathematician. An associate of the [[Bourbaki group]] and at one time a colleague of [[Alexander Grothendieck]], his interests have ranged over [[algebraic geometry]], [[representation theory]], [[mathematical physics]], and [[category theory]].

==Life and career==
Cartier was born on 10 June 1932. He studied at the [[École Normale Supérieure]] in [[Paris]] under [[Henri Cartan]] and [[André Weil]].<ref>{{MathGenealogy |id=56562 |name=Pierre Cartier }}</ref> After his 1958 [[thesis]] on algebraic geometry, he worked in a number of fields. He is known for the introduction of the [[Cartier operator]] in algebraic geometry in characteristic ''p'', and for work on duality of [[abelian varieties]] and on [[formal group]]s. He is the eponym of [[Cartier divisor]]s and [[Cartier duality]].

From 1961 to 1971, he was a professor at the [[University of Strasbourg]].  In 1970 he was an Invited Speaker at the [[International Congress of Mathematicians]] in [[Nice]].<ref>{{cite book|author=Cartier, Pierre|chapter=Groupes formels, fonctions automorphes et fonctions zeta des courbes elliptiques|title=''In:'' Actes des Congrés intern. Math.|volume=tome 2|pages=291–299|year=1970|chapter-url=http://www.mathunion.org/ICM/ICM1970.2/Main/icm1970.2.0291.0306.ocr.pdf|access-date=2017-11-14|archive-date=2017-07-06|archive-url=https://web.archive.org/web/20170706082401/http://www.mathunion.org/ICM/ICM1970.2/Main/icm1970.2.0291.0306.ocr.pdf|url-status=dead}}</ref>  He was awarded the 1978 [[Prize Ampère]] of the [[French Academy of Sciences]].<ref>{{cite web|date=18 October 2016|title=40 ans du Prix Ampère|url=https://www.academie-sciences.fr/pdf/prix/ampere_181016.pdf|website=Académie des sciences}}</ref> In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref>

Cartier died in [[Marcoussis]] on 17 August 2024, at the age of 92.<ref>[https://www.lemonde.fr/disparitions/article/2024/08/19/pierre-cartier-mathematicien-francais-est-mort_6286756_3382.html Pierre Cartier, mathématicien français, est mort] ''Le Monde'' {{in lang|fr}}</ref>

==Publications==
* {{cite book|url=https://books.google.com/books?id=EDV7CwAAQBAJ| title=Problèmes combinatoires de commutation et réarrangements | isbn=9783540360940 | last1=Cartier | first1=Pierre | last2=Foata | first2=Dominique | author-link2=Dominique Foata|date=14 November 2006 |publisher=Springer}} (1st edition 1969)<ref>{{cite web|title=''Commutation and Rearrangements'', An electronic reedition of the monograph: ''Problèmes combinatoires de commutation et réarrangements'' by Pierre Cartier and Dominique Foata|website=European Mathematical Information Service (EMIS)|url=https://www.emis.de/journals/SLC/books/cartfoa.html}}</ref>
* {{cite book|chapter=''An introduction to zeta functions'' by Pierre Cartier|pages=1–63|chapter-url=https://books.google.com/books?id=LvruCAAAQBAJ&pg=PA1| title=From Number Theory to Physics | isbn=9783662028384 | editor1=Waldschmidt, Michel | editor2=Moussa, Pierre | editor3=Luck, Jean-Marc | editor4=Itzykson, Claude | date=9 March 2013 | publisher=Springer}} (1st edition 1992)
* {{cite journal|date=September 2006|title=A primer of Hopf algebras|journal=Report Number IHES-M-2006-40|pages=1–74|url=https://people.math.osu.edu/kerler.2/VIGRE/InvResPres-Sp07/Cartier-IHES.pdf}}
* ''Freedom in Mathematics'', Springer India, 2016 (with [[Cédric Villani]], [[Jean Dhombres]], Gerhard Heinzmann), {{ISBN|978-81-322-2786-1}}.<ref>{{cite web|author=Glass, Darren|title=Review of ''Freedom in Mathematics'' by Pierre Cartier, Jean Dhombres, Gerhard Heinzmann, and Cédric Villani|date=July 7, 2016|website=MAA Reviews, Mathematical Association of America|url=https://www.maa.org/press/maa-reviews/freedom-in-mathematics}}</ref>
** Translation from the French language edition: ''Mathématiques en liberté'', La Ville Brûle, Montreuil 2012, {{ISBN|978-23-601-2026-0}}.
* Pierre Cartier: ''Alexander Grothendieck. A country known only by name.'' Notices AMS, vol. 62, 2015, no. 4, pp.&nbsp;373–382, [https://www.ams.org/notices/201504/rnoti-p373.pdf PDF.]

===As editor===
* {{cite book|url=https://books.google.com/books?id=XnaiG1GvbD8C| title=The Grothendieck Festschrift, Volume III: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck | isbn=9780817645762 | editor=Cartier, Pierre | editor2=Illusie, Luc | editor3=Katz, Nicholas M. | editor4=Laumon, Gérard | editor5=Manin, Yuri I. | editor6=Ribet, Kenneth A. | date=23 October 2007 | publisher=Springer}} (1st edition 1990)
* {{cite book|url=https://books.google.com/books?id=DNTZ_E5Nv9UC| title=Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization | isbn=9783540303084 | editor=Cartier, Pierre É. | editor2=Julia, Bernard | editor3=Moussa, Pierre | editor4=Vanhove, Pierre | date=18 July 2007 | publisher=Springer}}

==See also==
*[[Cotangent complex]]
*[[Dieudonné module]]
*[[MacMahon's master theorem]]

==References==
{{reflist}}

==External links==
{{wikiquote}}
*[https://www.ihes.fr/~cartier/ Cartier's website] at the [[Institut des Hautes Études Scientifiques]], with a photograph, CV, and list of publications
*[https://www.ams.org/distribution/mmj/vol4-1-2004/dedication.html Issue of Moscow Mathematical Journal dedicated to Pierre Cartier]
* {{MacTutor Biography|id=Cartier|title=Pierre Émile Jean Cartier}}
* [http://jfresan.files.wordpress.com/2009/11/the-castle-of-groups.pdf Javier Fresán ''The Castle of Groups'', Interview with Pierre Cartier, EMS Newsletter 2009, pdf]
*{{cite web|title=Pierre Cartier: Logarithmic divergences, ...|date=December 4, 2014|publisher=Hausdorff Center for Mathematics|website=YouTube|url=https://www.youtube.com/watch?v=_-5MyGUZ2TM}}
*{{cite web|title=Pierre Cartier. Schemes|date=November 29, 2015|publisher=ERC PhiloQuantumGravity|website=YouTube|url=https://www.youtube.com/watch?v=etdvnswIhMw}}
*{{cite web|title=Pierre Cartier - Conférence inaugurale|date=December 3, 2015|publisher=Institut des Hautes Études Scientifiques (IHÉS)|website=YouTube|url=https://www.youtube.com/watch?v=LYvjQgrC1kA}}
*{{cite web|title=Pierre Cartier: Is History of Mathematics a Part of General History|date=May 10, 2018|publisher=Prague Axiomatic Circle|website=YouTube|url=https://www.youtube.com/watch?v=cSonPdYgI3w}}
*{{cite journal|last1=Connes|first1=Alain|last2=Kouneiher|first2=Joseph|title=Pierre Cartier: A Visionary Mathematician|journal=Notices of the American Mathematical Society|date=May 2025|volume=72|issue=5|pages=514–522|url=https://www.ams.org/journals/notices/202505/rnoti-p514.pdf|doi=10.1090/noti3140|doi-access=free}}

{{Authority control}}

{{DEFAULTSORT:Cartier, Pierre}}
[[Category:1932 births]]
[[Category:2024 deaths]]
[[Category:People from Sedan, Ardennes]]
[[Category:Lycée Saint-Louis alumni]]
[[Category:École Normale Supérieure alumni]]
[[Category:Academic staff of the University of Strasbourg]]
[[Category:20th-century French mathematicians]]
[[Category:21st-century French mathematicians]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Nicolas Bourbaki]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Research directors of the French National Centre for Scientific Research]]
[[Category:University of Paris alumni]]
[[Category:Algebraic geometers]]
[[Category:Category theorists]]


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