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Topic: Flat morphism

	Flat morphism - Wikpedia (Site not responding. Last check: 2007-10-22)
		Two of the basic intuitions are that flatness is a generic property, and that the failure of flatness occurs on the jumping set of the morphism.
		It turns out (retrospectively) that flatness in morphisms is directly related to controlling this sort of semicontinuity, or one-sided jumping.
		Flat morphisms are used to define (more than one version of) the flat topos, and flat cohomology of sheaves from it.
	www.bostoncoop.net /~tpryor/wiki/index.php?title=Flat_morphism (298 words)

	Flat module -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		Therefore, the R-module M is flat if and only if for any (additional info and facts about injective) injective (Similarity of form) homomorphism K → L of R-modules, the induced homomorphism K⊗M → L⊗M is also injective.
		Lazard proved in 1969 that a module M is flat if and only if it is a (additional info and facts about direct limit) direct limit of (additional info and facts about finitely-generated) finitely-generated (additional info and facts about free module) free modules.
		Flatness may also be expressed using the (additional info and facts about Tor functor) Tor functors, the (additional info and facts about left derived functors) left derived functors of the tensor product.
	www.absoluteastronomy.com /encyclopedia/f/fl/flat_module.htm (617 words)

	flat module (Site not responding. Last check: 2007-10-22)
		In abstract algebra, a flat module for a ring R is an R-module M such that taking the tensor product over R with M preserves exact sequences.
		Over a Noetherian local ring, flatness, projectivity, and freeness are all equivalent.
		In the case when R is a commutative ring, one can say that flatness for an R-module M is equivalent to tensor product with M being an exact functor from the category of R-modules to itself.
	www.yourencyclopedia.net /flat_module.html (215 words)

	Flats In Paris (Site not responding. Last check: 2007-10-22)
		Under equal temperament, ''C flat'' is the same as, or enharmonically equivalent to, ''B'' and ''F flat'' is the same as ''E''.
		In musical tuning, flat can also mean "very slightly lower in pitch." If two strings are slightly out of tune, the lower-pitched one is said to be flat with respect to the other.
		The flatness of a surface is the degree to which it approximates a mathematical plane.
	www.blownspeakers.com /pages3/33/flats-in-paris.html (821 words)

	[No title]
		A 1- morphism of flat Hopf algebroids from (X0, X1) to (Y0, Y1) is a pair of morphis* *ms of affine schemes fi : Xi -!
		A morphism P as in definition 1 is called a presentation of X. As far as we are* * aware, this definition of "algebraic" is due to P. Goerss [G ] and is certainly motivated by the equivale* *nce given in subsection 2.3 below.
		iii) ff is faithfully flat and fi is an isomorphism.
	hopf.math.purdue.edu /Naumann/comodlandweber.txt (5917 words)

	Flat morphism - Encyclopedia Glossary Meaning Explanation Flat morphism (Site not responding. Last check: 2007-10-22)
		Flat morphism - Encyclopedia Glossary Meaning Explanation Flat morphism.
		is a flat map for all P in X.
		This is a deep-lying theory, and has not been found easy to handle.
	www.encyclopedia-glossary.com /en/Flat-morphism.html (373 words)

	Centennial Celebration of Commutative Algebra (Site not responding. Last check: 2007-10-22)
		A ring morphism $A \to B$ is called a chain morphism if arbitrary chains of prime ideals of $A$ can be lifted through $A \to B$.
		As a main result, we have that universally subtrusive morphism (a special class of submersive morphisms like injective integral morphisms, pure morphisms or lying-over universally going-down morphisms) are universally chain morphisms.
		Then a ring morphism $A \to B$ has generalized going-down if an arbitrary local chain $X = \{P\sb i\}\sb{i\in I}\subset Spec(A)$ where $U(X)$ is dominated by a prime ideal $Q$ of $B$ is dominated by a local chain $Y = \{Q\sb i\}\sb{i\in I}\subset Spec(B)$ such that $U(Y) = Q$.
	www.math.unl.edu /events/cacentennial/abstracts.htm (1550 words)

	[No title]
		Theorem A. Suppose (A,) is a flat Hopf algebroid and B is a Landweber exact A-algebra.
		Suppose (A,) is a flat Hopf algebroid, and B is a Landweber exact A-algebra.
		Torsion theories of BPBP -comodules Suppose (A,) is a flat* Hopf algebroid, and B is a Landweber exact A-algebra.
	hopf.math.purdue.edu /Hovey-Strickland/torsion-comod.txt (8546 words)

	PlanetMath: flat morphism
		is flat, then this family should be thought of as a ``continuous family''.
		This is version 1 of flat morphism, born on 2004-02-23.
		(Algebraic geometry :: Foundations :: Schemes and morphisms)
	planetmath.org /encyclopedia/Flat3.html (72 words)

	Glossary of scheme theory (Site not responding. Last check: 2007-10-22)
		A morphism f is an open immersion if locally it is of the form of an inclusion of an affine open subset.
		A deep property of proper morphisms is the existence of a Stein factorization, namely the existence of an intermediate scheme such that a morphism can be expressed as one with connected fibres, followed by a finite morphism.
		A separated morphism is a morphism f such that the fiber product of Y with itself along f has its diagonal as a closed subscheme — in other words, the diagonal map is a closed immersion.
	www.worldhistory.com /wiki/G/Glossary-of-scheme-theory.htm (884 words)

	Appendix by J. Cremona and B. Mazur: ``Explaining'' Shafarevich-Tate via Mordell-Weil
		Viewing (1) as an exact sequence of sheaves for the flat topology, and passing to the associated cohomology sequence we see that (2) may be thought of, ambiguously as computed for either the étale or the flat topology.
		be the evident quotient (quasi-finite flat) group scheme, and noting that, by construction, its special fiber is trivial.
		However, the cokernel of this morphism restricted to the fiber in characteristic
	modular.fas.harvard.edu /papers/shacomp/shacomp6/node24.html (1383 words)

	[No title]
		## A morphism is stored as a list of the images of its values on a set ## of numbers, which form its domain of definition, and are taken to be ## an object in a concrete category.
		For every object there should be ## at least one generator morphism whose support is that object.
		At the moment it will not work unless for every object there ## is at least one generator morphism whose support is that object.
	www.math.umn.edu /~webb/GAPfiles/categories (1459 words)

	Footrot Flats -- Recommendations and Resources (Site not responding. Last check: 2007-10-22)
		It ran from 1975 until 1999 in newspapers around the world, and resulted in a series of 27 books (collecting the newspaper strips, with additional material), a stage musical, and an animated feature film called ''Footrot Flats: the Dog's Tale''.
		The cartoon was based around the life of Wal Footrot's sheep dog, "Dog", on their farm Footrot Flats (hence the title), and the other characters, human and animal, that came into their lives.
		Dog's thoughts are voiced in thought bubbles, though he is clearly "just a dog" rather than the anthromorphised creatures sometimes found in other comics or animation.
	www.becomingapediatrician.com /health/59/footrot-flats.html (1148 words)

	[No title]
		A brief foray to EGA IV_1.1 1.1 Quasicompact morphisms 1.2 Quasiseparated morphisms 1.3 Morphisms locally of finite type 1.4 Morphisms locally of finite presentation 1.5 Morphisms of finite type 1.6 Morphisms of finite presentation, 1.7 Bettering earlier results (i.e.
		EGA IV_1.1 1.8 Morphisms of finite presentation and constructible sets 1.9 Pro-constructible and ind-constructible sets if time: 1.10 Application to open morphisms EGA II.
		3.7 Morphisms from a prescheme to a Spec.
	math.stanford.edu /~vakil/egasummary (629 words)

	Flat map - Encyclopedia Glossary Meaning Explanation Flat map (Site not responding. Last check: 2007-10-22)
		Flat map - Encyclopedia Glossary Meaning Explanation Flat map.
		Here you will find more informations about Flat map.
		In ring theory, a homomorphism f from a ring R to a ring S is flat if S becomes a flat R-module when the action of R on S is given by f.
	www.encyclopedia-glossary.com /en/Flat-map.html (109 words)

	ABSTRACTS FOR ANNAPOLIS ALGEBRAIC GEOMETRY CONFERENCE CONTRIBUTED TALKS (Site not responding. Last check: 2007-10-22)
		Given a flat, projective morphism Y -> T from an equidimensional scheme to a nonsingular curve and a subscheme Z of Y, we provide conditions under which specialization of the Segre class s(N_Z,Y) of the normal cone of Z in Y implies flatness of the normal cone.
		We apply this result to study when the relative tangent star cone of a flat family is flat, and consider examples involving flat families of stick figures.
		We discuss the relation between a square-free monomial ideal in a polynomial ring and a certain simplicial complex associated to that ideal.
	mathweb.mathsci.usna.edu /faculty/Conferences/AlgGeom2001/contrib.html (1340 words)

	AMCA: Pure morphisms of schemes by Bachuki Mesablishvili (Site not responding. Last check: 2007-10-22)
		We prove that, for any morphism f : R --> S of commutative rings, the induced morphism f* : Spec(S) --> Spec(R) of affine schemes is pure iff f is pure as a morphism of R-modules.
		A quasi-compact morphism of schemes is an effective descent morphism [5] with respect to the (SCH)
		The sufficient part of the theorem generalizes Grothendieck's result that faithfully flat quasi-compact morphisms of schemes are effective descent morphisms [6].
	at.yorku.ca /c/a/j/f/32.htm (326 words)

	PlanetMath:
		finite type (in finite morphism) owned by rmilson
		flat sheaf (in flat morphism) owned by archibal
		Frobenius morphism (in Frobenius morphism) owned by alozano
	planetmath.org /encyclopedia/F (1711 words)

	UWO Algebra Seminar
		p : M --> A. p is the universal morphism from M to an affine, torus embedding monoid.
		Vinberg calls M /flat/ if p is a flat morphism with reduced and irreducible
		trivial divisor class group is a flat monoid.
	www.math.uwo.ca /~masoud/cv/algsem.html (2095 words)

	AIF : Tome 49 fascicle 2 -- 1999
		If is not a projective space, then the degree of a morphism
		In particular, to prove our main theorem we show the non-existence of a flat 3-dimensional projective variety with
		Key words : smooth projective threefold, finite morphism, flat variety
	annalif.ujf-grenoble.fr /Vol49/E492_2/E492_2.html (122 words)

	8.7 Action of correspondences (Site not responding. Last check: 2007-10-22)
		X is a morphism then the pull-back sequence of vector space schemes
		However, if V is a vector bundle then the pull back sequence of vector space schemes is exact regardless of the nature of the morphism Y
		Thus we see that for any correspondence from a projective scheme X to a scheme Y we obtain a homomorphism
	www.imsc.ernet.in /~kapil/crypto/notes/node45.html (391 words)

	abstract 2003-07 (Site not responding. Last check: 2007-10-22)
		More precisely, we give the characteristic polynomials of the Frobenius endomorphism on the étale
		Finally, as an analogue of Artin's holomorphy conjecture, we prove that, if Y —> X is a finite flat morphism between two varieties over a finite field, then the characteristic polynomial of the Frobenius morphism on H
		We are then enable to give an estimation for the number of rational points in a flat covering of curves.
	iml.univ-mrs.fr /editions/preprint2003/abstracts/abstract2003-07.html (113 words)

	9.5 Frobenius Endomorphism (Site not responding. Last check: 2007-10-22)
		From this one can show that the intersection of the diagonal
		, the Frobenius F is a flat morphism and thus gives an endomorphism of K
		The latter group thus acquires some ``structure'' in addition to being an abelian group.
	www.imsc.ernet.in /~kapil/crypto/notes/node52.html (490 words)

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