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Grothendieck's political views were radical and pacifist.

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## Some Related Sentences

Grothendieck's and .

At the time of his birth

__Grothendieck's__mother was married to Johannes Raddatz, a German journalist,**and**his birthname was initially recorded as Alexander Raddatz__.__
Alexander

__Grothendieck's__work during the ` Golden Age ' period at IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory**and**complex analysis__.__
While the issue of military funding was perhaps the most obvious explanation for

__Grothendieck's__departure from IHÉS, those who knew him say that the causes of the rupture ran deeper__.__
While Grothendieck was at the IHÉS, opposition to the Vietnam War was heating up,

**and**Cartier suggests that this also reinforced__Grothendieck's__distaste at having become a mandarin of the scientific world__.__
The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite dimensional ;

__Grothendieck's__theorem shows that the higher direct images of coherent sheaves under a proper map are coherent ; this reduces to Serre's theorem over a one-point space__.__
Perhaps

__Grothendieck's__deepest single accomplishment is the invention of the étale**and**l-adic cohomology theories, which explain an observation of André Weil's that there is a deep connection between the topological characteristics of a variety**and**its diophantine ( number theoretic ) properties__.__
This program culminated in the proofs of the Weil conjectures, the last of which was settled by

__Grothendieck's__student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics__.__
There is a natural way to associate a site to an ordinary topological space,

**and**__Grothendieck's__theory is loosely regarded as a generalization of classical topology__.__
However, most modern algebraic geometry texts starting with Alexander

__Grothendieck's__foundational EGA use the convention in this article .< ref > A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud ( 1995 ), which uses " h < sub > A </ sub >" to mean the covariant hom-functor__.__
Thus, V ( S ) is " the same as " the maximal ideals containing S

__.____Grothendieck's__innovation in defining Spec was to replace maximal ideals with all prime ideals ; in this formulation it is natural to simply generalize this observation to the definition of a closed set in the spectrum of a ring__.__
However,

__Grothendieck's__standard conjectures remain open ( except for the hard Lefschetz theorem, which was proved by Deligne by extending his work on the Weil conjectures ),**and**the analogue of the Riemann hypothesis was proved by, using the étale cohomology theory but circumventing the use of standard conjectures by an ingenious argument__.__
This is done by studying the zeta functions of the even powers E < sup > k </ sup > of E

**and**applying__Grothendieck's__formula for the zeta functions as alternating products over cohomology groups__.__
pointed out that a generalization of Rankin's result for higher even values of k would imply the Ramanujan conjecture,

**and**Deligne realized that in the case of zeta functions of varieties,__Grothendieck's__theory of zeta functions of sheaves provided an analogue of this generalization__.__
* was able to prove the hard Lefschetz theorem ( part of

__Grothendieck's__standard conjectures ) using his second proof of the Weil conjectures__.__
;

__Grothendieck's__Galois theory: A very abstract approach from algebraic geometry, introduced to study the analogue of the fundamental group__.__
A

__.__L__.__Rosenberg has created a rather general relative concept of noncommutative quasicompact scheme ( over a base category ), abstracting the__Grothendieck's__study of morphisms of schemes**and**covers in terms of categories of quasicoherent sheaves**and**flat localization functors__.__
The term prescheme has fallen out of use, but can still be found in older books, such as

__Grothendieck's__Éléments de géométrie algébrique**and**Mumford's__.__
In mathematics,

__Grothendieck's__Galois theory is a highly abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry__.____Grothendieck's__use of these universes ( whose existence cannot be proved in ZFC ) led to some uninformed speculation that étale cohomology

**and**its applications ( such as the proof of Fermat's last theorem ) needed axioms beyond ZFC

__.__

political and views

In the 1930s, Carrel

**and**Charles Lindbergh became close friends not only because of the years they worked together but also because they shared personal,__political__,**and**social__views__**.**
Reading about famous oratory aroused Johnson's interest in

__political__dialogue**and**private debates with customers having opposing__views__on issues of the day**.**
Supporters of this view believe that “ to a hypothetical outside reader, presents Christianity as enlightened, harmless, even beneficent .” Some believe that through this work, Luke intended to show the Roman Empire that the root of Christianity is within Judaism so that the Christians “ may receive the same freedom to practice their faith that the Roman Empire afforded the Jews .” Those who support the view of Luke ’ s work as

__political__apology generally draw evidence from the facts that Christians are found innocent of committing any__political__crime ( Acts 25: 25 ; 19: 37 ; 19: 40 )**and**that Roman officials ’__views__towards Christians are generally positive**.**
Although Franklin apparently reconsidered shortly thereafter,

**and**the phrases**were**omitted from all later printings of the pamphlet, his__views__may have played a role in his__political__defeat in 1764**.**
His anti-fascist

__political____views__caused him a great deal of trouble with the establishment in Hungary**.**
During recent times, mainly during the apartheid reform

**and**post-1994 eras, many more white Afrikaans-speaking people, mainly with " conservative "__political____views__**and**of Trekboer**and**Voortrekker descent, have preferred to be called " Boers " or Boere-Afrikaners, rather than " Afrikaners ".
During the 1960s the

__political__atmosphere began to gradually change,**and**attention was once again directed to Chaplin's films instead of his__political____views__**.**
The honour had already been proposed in 1931

**and**1956, but was vetoed after a Foreign Office report raised concerns over Chaplin's__political____views__**and**private life ; it was felt that honouring him would damage both the reputation of the British honours system**and**relations with the United States**.**
Although the project started in 1958, Chaplin only received his star in 1970 because of his

__political____views__**.**
Michael Kelly, a Washington Post journalist

**and**critic of anti-war movements on both the left**and**right, coined the term " fusion paranoia " to refer to a__political__convergence of left-wing**and**right-wing activists around anti-war issues**and**civil liberties, which he said**were**motivated by a shared belief in conspiracism or anti-government__views__**.**
Hearst's critics often assumed that all the strips in his papers

**were**fronts for his own__political__**and**social__views__**.**
Other utilitarian-type

__views__include the claims that the end of action is survival**and**growth, as in evolutionary ethics ( the 19th-century English philosopher Herbert Spencer ); the experience of power, as in despotism ( the 16th-century Italian__political__philosopher Niccolò Machiavelli**and**the 19th-century German Friedrich Nietzsche ); satisfaction**and**adjustment, as in pragmatism ( 20th-century American philosophers Ralph Barton Perry**and**John Dewey );**and**freedom, as in existentialism ( the 20th-century French philosopher Jean-Paul Sartre ).
Mohism though popular at first due to its emphasis on brotherly love versus harsh Qin Legalism, fell out of favour during the Han Dynasty due to the efforts of Confucians in establishing their

__views__as__political__orthodoxy**.**
Psychologist Felicia Pratto

**and**her colleagues have found evidence to support the idea that a high Social Dominance Orientation ( SDO ) is strongly correlated with conservative__political____views__,**and**opposition to social engineering to promote equality, though Pratto's findings have been highly controversial**.**
Modern history has rejected these

__views__, instead characterising Domitian as a ruthless but efficient autocrat, whose cultural, economic**and**__political__program provided the foundation of the peaceful 2nd century**.**
As more

**and**more of its demands**were**met during the 1990s – such as the direct popular election of Taiwan's president**and**all representatives in its Legislative Yuan,**and**open discussion of Taiwan's repressive past as represented in the 2-28 Incident**and**its long martial law aftermath – a greater variety of__views__could be advocated in the more liberal__political__atmosphere**.**
In 1980 Susan Wirth, a 35 year old teacher living in San Francisco, was abducted by her parents to be deprogramed from her leftist

__political____views__**and**activities**.**
The official opposition

**and**__political__pressure groups, like the Muslim Brotherhood,**were**active in Egypt**and**made their__views__public**.**
In addition to the formal structure of the ELDR Party, there are convened at least two Political Leaders ' Meetings a year in order to exchange

__views__on the items on the agenda of the European Council**and**more general__views__on the European__political__situation**.**
Environmental NGOs vary widely in

__political____views__**and**in the amount they seek to influence the environmental policy of the United States**and**other governments**.**0.103 seconds.