synonymGrossendick(French algebraic geometer) generally refers to Alexander Grottendick
Grothendieck, Alexander,StatelessnessPersonFrance, bornGermany。One of the greatest mathematicians in the 20th century, but he is basically an alternative, far away from mathematicians in academia.He hasn't sufferedregular educationHe did not step up the academic ladder step by step, and completely separated from the academic world after 1970.
Alexander Grothendieck, on March 28, 1928GermanyBerlinbirth[1]，judeaHe is a stateless mathematician of Chinese descent. In 1966, he was awardedFields Medal He created a whole set of modernAlgebraic geometryabstractTheoretical system, YesHomological algebraThere are also achievements.He is one of the greatest mathematicians in the 20th century, but he is basically an alternative, far away from mathematicians in academia.He did not receive formal education, nor did he step up the academic ladder step by step, and he completely separated from academia after 1970.
parent
Grotendick's father was a Jew, probably Alexander Shapiro, who usedSashaOne, born in 1890Russia、Belarus、UkraineBorder.At the age of 15, he was recruited by anti government organizations to participate in anti government activitiesczarstruggle.He was later arrested and sentenced to death at first, but was sentenced to life imprisonment because of his youth.He spent the next ten years in prison, fled in chaos and joined the anti government peasant army in Ukraine.
He married a Jewish woman and gave birth to a son, but he was very romantic and busy with marriage.In one operation, he lost his left arm and escaped with the help of many women and comrades under the pseudonym Alexander TanaRoveArrive successivelyBerlinAnd Paris.After returning to Berlin, he met Hanka Grotendick, a married woman who was born in Hamburg and believed in Protestantism. The couple gave birth to Alexander Grotendick, originally named Alexander Radac, who was the surname of Hanka's husband.They formed a "family" with their son and Hanka's legitimate daughter.
Character's Life
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childhood
Hanka and Sasha hope to become writers and contact radicals from all sides.In 1933,Nazi PartyThey were forced to leave Germany for Spain.In 1936, they participatedpopular front(Frente Popular).Alexander Grotendick lived in the home of a German priest who was the headmaster of a school near Hamburg.In 1939, he andParents inFrance reunites.They were arrested and deported.Sasha is imprisoned in FranceAlege ProvinceWernerconcentration camp, then forward toAuschwitz Concentration Camp Was killed in 1942.Hanka and Alexander Grotendick were taken to FranceLozierRiekro concentration camp.
The war is overLater, Alexander Grotendick and his mother lived inMontpellierNearby.Because of Alexander Grotendick's financial aid, their life is stable.He registeredMathematics, but seldom take classes. I like to study the concept of volume in one corner.(As he explained in "Harvest and Sowing", these initial studies are the beginning of his independent research and also lead him to rediscoverLebesgue integral。）One used to followEli JiadangProfessor, send Alexander Grotendick to Paris with a letterrecommendation。It was not Eli Gardang who received him there, but his sonHenri Cartan 。Henry Gardang dominated France at that timeHigher Normal School(Eacute; cole normal sup é rieure) is also responsible for the famous Jiadang research class.Alexander Grotendick felt that he was the only mathematician in the world until he found the elites in Paris.
Years in IHES
When he came to the IHES Institute in the south of Paris, which was built in 1958, his wonderful Grotendik Riemann Roch theorem began to attract people's attention, followed by a series of high-yielding seminars.Grotendick himself did not actually follow the traditional route of publishing articles in magazines;However, he gathered a powerful school, and its dominance in mathematics lasted for ten years.
He avoided Paris and arrivedNanxi，Assignment·DieudoneandLaurent Schwartz To prepare his thesis.During that time, he wrote six articles, and he chose one "Produits tensors topologiques et spaces nucl é aires" as his paper.After Laurent Schwartz introduced Alexander Grotendick's work in Paris, Alexander Grotendick joinedBulbakiGroup, stay in the group for many years.He has no nationality because of his father, so he has difficulty in finding a job.His stateless status made him unable to hold public office, and the only way to become a citizen was to serve in the military, but he refused to do so, so he had to find another way out.He left France, served as a guest professor in Brazil from 1953 to 1955, and then came to the United States in 1956Kansas。During this period, he changed his research topic.
In hisfunctional analysisAfter excellent work, Alexander Grotendick turned toAlgebraic geometry。He revolutionized the subject, andJean-Pierre Serre Cooperate to establish a new foundation and introduce the concept of concept.They communicate a lot. Although they have opposite styles, they can complement each other and achieve results.He returned to Paris in 1956, preferringtopologyAnd algebraic geometry.He created a new version of Riemann Roch theorem, revealingAlgebraic varietyThe hidden relationship between the topological and analytic properties of.
After his mother died in 1957, he felt depressed for many months.The next year he decided to stop the unfinished work and achieve some amazing breakthroughs.He also met his future wife and had three children with her.
For math andTheoretical physicsEstablished by researchFrench Institute of Advanced Sciences(Institut des hautes é tunes sciences) Receive him.There he met Jean DionneRene Thorn Louis Michel and David Rueller, and set about establishing the theory of algebraic geometry.
In 1958, he was invited toInternational Congress of MathematiciansThe content of the 1-hour report is not so much a summary of the known content of the discipline at that time as a forecast of the work he will do in the next 10 years.From 1960 to 1967, he co wrote《Fundamentals of Algebraic Geometry》(É l é ments de g é om é trie alg é brique).His Algebraic Geometry Seminar organized and published 7 volumes of SGA.
In 1966, he won the Fields Prize, but he refused to go toSoviet UnionReceive awards.From 1967 toVietnam?Travel,Prague SpringThe events in May 1968 led him to join the opposition until 1970, when he quit his job at the French Institute of Advanced Science to protest that part of its funding came from the Ministry of Defence.
After mathematics, radical ecological protector
After his resignation, he founded Survivre et vivre to promote his anti war and ecological protection ideas.He was abandoned by the mathematics worldCollege de France andFrench National Centre for Scientific Research's job applications were rejected.He divorced and established a community near Paris with Justina Barbie, a doctoral student he met in the United States.
In 1973, they moved toEero ProvinceAnd experiment with anti orthodox culture.Justina Barbie gave birth to a child and left him shortly afterwards.He gotUniversity of Montpellier He was employed as a professor and remained in office until his retirement in 1988.
From 1980 to 1995, he wrote four books: La longue marche à traders lath é orie de Galois, Esquisse d'un programme,À la poursuite des champs and Les d é rivateurs.But the most famous is his autobiographical book "R é coltes et Semailles" (about 2000 pages) written in 1985.He wrote that he experienced three emotions in his life: women, mathematics and meditation.
The awards given to researchers are too highsocial positionAnd reputation;
He has been away from the scientific community since 1970 (the award is for his work 25 years ago).
He is a pacifist (some research is directly or indirectly funded by the military)
He also refused to congratulate him on his 60th birthdayBirthdayAnd the edited anthology《The Grothendieck Festschrift》(published in 1990), because he believed that his work was not well understood.
In 1990, he left all his mathematical writing manuscripts and settled down inPyrenees。Since then, he has lived in seclusion, completely cut off from the research community.
In 2010, he asked for a ban on the dissemination of all his works.HisfansAll electronic versions of the manuscript and his other works were deleted from the Internet[2]。
Scientific achievements
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Alexander Grotendick's contribution to algebraic geometry is extensive and profound, which can be roughly divided into 10 aspects: (1) continuous and discreteDuality(Seeking category, 6 kinds of calculus);(2) Riemann Loch Grotendick theorem, which puts Riemann Loch definite reasonAlgebraic curveGeneralization of Sum Algebraic Chimney to ArbitraryHigh-dimensional algebraic varietyDuring which Tuopu K theory was developed;(3) The introduction of the concept of general form reduces algebraic geometry to commutativeAlgebra；(4) Topological theory;（5）etale cohomology Cohomology with L;(6) Dynamic theory;(7) Crystallographic cohomology;(8) Cohomology of topology;(9) Stable topology;(10) Non AbelAlgebraic geometry。He and othersCo publishingMore than a dozen great books, more than 10000 pages in total, have become the bible of algebraic geometry.
personnel training
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Grotendick's most famous students arePierre Deligne And Michelle Renault.
Social expectations
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So far, there are still many ideas in Grotendick's writings that have not been fully understood, but have produced many big results, such as Delin's proof of Weiyi conjecture andK theoryThe birth of.In 1984, Grotondick's manuscript "Draft Programme" was circulated among some mathematicians, and was officially published in 1994. Its content has yet to be discovered. In 1988SwedenHe refused to receive the Crafoord Prize awarded by the Academy of Sciences, and denounced the current corruption in academic circles.However, many colleagues and students still continue his work.
