
	Where results make sense

Topic: Grothendieck topology

Related Topics

Grothendieck topos

Presheaf

Yoneda lemma

Etale cohomology

Shelah cardinal

Ramsey cardinal

Algebraic geometry

Topology

Huge cardinal

Extendible cardinal

Topos

Grothendieck

Subtle cardinal

Alexander Grothendieck

List of publications in mathematics

In the News (Mon 30 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	NationMaster - Encyclopedia: Grothendieck topology
		The topology on Spc induces a topology on Spc/X.
		Sheaf theory Alexander Grothendieck (born March 28, 1928, Berlin) is one of the greatest mathematicians of the 20th century, with major contributions to algebraic geometry, homological algebra, and functional analysis.
		In mathematics, a Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C, and with that the definition of general cohomology theories.
	www.nationmaster.com /encyclopedia/Grothendieck-topology (4742 words)

	Topology Encyclopedia (Site not responding. Last check: 2007-10-16)
		Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry.
		The most basic division within topology is into point-set topology, which investigates such concepts as compactness, connectedness, countability, and algebraic topology, which investigates such concepts as homotopy, homology, and knot theory.
		In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
	www.hallencyclopedia.com /topic/Topology.html (1819 words)

	Grothendieck biography
		Grothendieck moved to France in 1941 and later entered Montpellier University.
		It is no exaggeration to speak of Grothendieck's years 1959-70 at the IHES as a 'Golden Age', during which a whole new school of mathematics flourished under Grothendieck's charismatic leadership.
		Grothendieck was always strongly pacifist in his views and campaigned against the military built-up of the 1960s.
	www-history.mcs.st-andrews.ac.uk /Biographies/Grothendieck.html (535 words)

	PlanetMath: Alexander Grothendieck
		Alexander Grothendieck (1928 -) German mathematician, one of the pioneers of topos theory.
		Two decades later, he declined the Crafoord Prize that was awarded to him and his student Pierre Deligne, because he didn't want the money and because the award was in recognition of work he had done much earlier in his career.
		This is version 1 of Alexander Grothendieck, born on 2007-01-26.
	planetmath.org /encyclopedia/AlexanderGrothendieck.html (149 words)

	The Spectator.co.uk
		In the first place, the luminous brilliance of Grothendieck’s mathematical achievement — his 1966 Fields Medal, the Nobel Prize of maths, is an indicator — is matched only by the near impossibility of explaining it to anyone without a background in pure maths.
		Grothendieck doesn’t write popularising books like Stephen Hawking; he doesn’t tour American universities lecturing undergraduates; and he doesn’t, any more, publish his researches and discoveries in mathematical journals.
		Grothendieck’s father was an anarchist who died in Auschwitz; Alexandre, along with his German mother Hanka, was interned in France during the war as an ‘undesirable’.
	www.lewrockwell.com /spectator/spec262.html (1224 words)

	Grothendieck topology
		In mathematics, a Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C, and with that the definition of general cohomology theories.
		Note that a Grothendieck topology is not a topology in the classical sense.
		This is the defining property of a sheaf, and a Grothendieck topology on C is an attempt to capture the essence of what is needed to define sheaves on C.
	www.teachersparadise.com /ency/en/wikipedia/g/gr/grothendieck_topology.html (625 words)

	Grothendieck topology - ExampleProblems.com (Site not responding. Last check: 2007-10-16)
		Grothendieck topologies are not comparable to the classical notion of a topology on a space.
		Grothendieck also saw how to phrase the definition of covering abstractly; this is where the definition of a Grothendieck topology comes from.
		A Grothendieck topology J on a category C is defined by giving, for each object c of C, a collection J(c) of sieves on c, subject to certain conditions.
	www.exampleproblems.com /wiki/index.php/Grothendieck_topology (1308 words)

	Letter from Grothendieck \| The n-Category Café
		Alexander Grothendieck was the most visionary and radical mathematician in the second half of the 20th century - at least before he left his home and disappeared one fine day in 1991.
		Leila Schneps, an expert on Grothendieck’s theory of dessins d’enfants and a founding member of the Grothendieck Circle, was one of the last mathematicians to meet Grothendieck and correspond with him.
		It is sad tht while Grothendieck was asking the right question: “what is the metre” and rightly saying that the convention c = 300,000,000 m/s would have been simpler the standard reaction to his query was to see there the clear symptom of a deranged mind.
	golem.ph.utexas.edu /category/2006/08/letter_from_grothendieck.html (1794 words)

	Grothendieck topology - Definition, explanation
		It is not a topology in the classical sense, and may not be equivalent to giving one (although it can be used to faithfully model sober spaces).
		At a time when cohomology for sheaves on topological spaces was well established, Alexander Grothendieck wanted to define cohomology theories for other structures, his schemess.
		This is the defining property of a sheaf (see gluing axiom) and a Grothendieck topology on C is an attempt to capture the essence of what is needed to define sheaves on C.
	www.calsky.com /lexikon/en/txt/g/gr/grothendieck_topology.php (850 words)

	Gatorsports.com :: 100 years of Gator Football (Site not responding. Last check: 2007-10-16)
		Grothendieck topologies are not comparable to the classical notion of topological spaces.
		The topology generated by the original collection of covering families is then the same as the topology generated by the pretopology, because the sieve generated by an isomorphism Y → X is Hom(−, X).
		The topology on Spc induces a topology on Spc/X.
	www.gatorsports.com /apps/pbcs.dll/section?template=wiki&text=Grothendieck_topology (3475 words)

	[No title]
		Thus, the la* n- guage of Grothendieck* topologies is becoming a necessary tool for the al* *gebraic topologist.
		Warning 3.1.Recall that the naive subspace topology may not be compactly gen- erated, hence "the subspace topology" refers to applying the Kelly functor k to* * this naive construction.
		Since both vertical maps are homeomorphisms, requiring Y to be a sheaf in the topology discussed in 3.5.2 is equivalent to demanding that Y0 is homeomorphic to nYn via the adjoint structure map.
	www.math.purdue.edu /research/atopology/JohnsonM/shfloop.txt (7069 words)

	Grothendieck biography
		Grothendieck moved to France in 1941 and later entered Montpellier University.
		Grothendieck spent the years 1953-55 at the University of Sao Paulo and then he spent the following year at the University of Kansas.
		He introduced the theory of schemes in the 1960s which allowed certain of Weil's number theory conjectures to be solved.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Grothendieck.html (535 words)

	Categorical Geometry Chapter 2 Section 2.3 Zhaohua Luo
		(a) A Grothendieck topology is unipotent iff any non-isomorphic initial map is not a cover and the empty set is a cover only on 0.
		If D is a divisor then the collection of D-covers form a Grothendieck topology on A.
		The collection of D-covers is a Grothendieck topology by (2.3.4).
	www.geometry.net /win95/sec2-3.html (568 words)

Try your search on: Qwika (all wikis)