
	Where results make sense

Topic: Motivic cohomology

Related Topics

cohomology of groups

tale cohomology

cohomology theories

etale cohomology

sheaf cohomology

Galois cohomology

Crystalline cohomology

Alexander Spanier cohomology

flat cohomology

Spencer cohomology

Cech cohomology

local cohomology

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Cohomology - Wikipedia, the free encyclopedia
		Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology.
		Cohomology arises from the algebraic dualization of the construction of homology.
		A cohomology theory is a family of contravariant functors from the category of pairs of topological spaces and continuous functions (or some subcategory thereof such as the category of CW complexes) to the category of Abelian groups and group homomorphisms that satisfies the Eilenberg-Steenrod axioms.
	en.wikipedia.org /wiki/Cohomology (705 words)

	Motivic cohomology - Wikipedia, the free encyclopedia
		Motivic cohomology is a homological theory in mathematics, the existence of which was first conjectured by Grothendieck during the 1960s.
		Serre, for example, preferred to work more concretely with a system of compatible l-adic representations, which at least conjecturally should be as good as having a motive, but instead listed the data obtainable from a motive by means of its 'realisations' in the etale cohomology theories with l-adic coefficients, as l varied over prime numbers.
		In some sense motivic cohomology would be the mother of all cohomology theories in algebraic geometry; the other cohomology theories would be specializations.
	en.wikipedia.org /wiki/Motivic_cohomology (283 words)

	Motivic Cohomology
		The collection of all the cohomology groups of a space forms a ring, and the same is true of the K-groups.
		Crucial work on motivic cohomolgy was done by Spencer Bloch, who established in certain special cases an analog of the Chern character in the algebraic setting.
		A remarkable achievement of Suslin and Voevodsky is that, after making a standard modification of the motivic cohomology and singular cohomology, they were able to prove that the modified motivic cohomology of X and the modified singular cohomology of X(C) are in fact isomorphic.
	e-math.ams.org /ams/mathnews/motivic.html (1302 words)

	Motivic Homotopy Theory Program (Site not responding. Last check: 2007-09-30)
		The motivic homotopy theory is the homotopy theory for algebraic varieties and, more generally, for Grothendieck's schemes which is based on the analogy between the affine line and the unit interval.
		Eventually, the motivic homotopy theory is expected to provide techniques which may help to solve problems in algebraic geomerty such as various "standard conjectures on algebraic cycles", Beilinson-Soule vanishing and rigidity conjectures, the Bloch-Kato conjecture etc.
		The triangulated categories of motives and the motivic stable homotopy categories are connected by pairs of adjoint functors.
	www.math.ias.edu /~vladimir/seminar.html (870 words)

	Lecture Notes on Motivic Cohomology
		Its purpose is to introduce Motivic Cohomology, develop its main properties and, finally, to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, étale cohomology and Chow groups.
		The notion of a motive is an elusive one, like its namesake the "motif" of Cezanne's impressionist method of painting.
		We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory.
	www.claymath.org /publications/Motivic_Cohomology (280 words)

	[No title]
		After a short introduction with a quotation of Grothendieck on the fascination of motives, the existence and compatibility of several cohomology theories is recalled.
		On the other hand, the apparent lack, in general, of compatibility isomorphisms between the various $\ell$-adic cohomology theories (for different values of the primes $\ell)$ is an unsatisfactory fact, and one feels that in many situations, e.g.
		In some cases a "motivic foobar" has a more specific meaning, either out of tradition or because it is part of the theory of motives that is known to make sense.
	www.math.niu.edu /~rusin/known-math/98/motivic (1182 words)

	Weil-etale motivic cohomology, by Thomas H. Geisser (Site not responding. Last check: 2007-09-30)
		As a consequence, we get a long exact sequence relating Weil-etale cohomology to etale cohomology, show that for finite coefficients the cohomology theories agree, and with rational coefficients a Weil-etale cohomology group is the direct sum of two etale cohomology groups.
		In the second half of the paper we restrict ourselves to Weil-etale cohomology of the motivic complex.
		We show that for smooth projective varieties over finite fields, finite generation of Weil-etale cohomology is equivalent to Weil-etale cohomology being an integral model of l-adic cohomology, and also equivalent to the conjunction of Tate's conjecture and (rational) equality of rational and numerical equivalence.
	front.math.ucdavis.edu /ANT/0351 (156 words)

	New Contexts for Stable Homotopy Theory
		The development of cohomology theories which behaved in positive characteristic like the classical cohomology used by Lefschetz was a major achievement of the 20th century.
		This exploitation of motivic homotopy theory in number theory and algebraic topology was spurred on by the programme, which also played an important role in spreading the developing body of knowledge.
		Elliptic cohomology is the third of a sequence of natural probes into the nature of high dimensional objects bringing together ideas from geometry, arithmetic and analysis.
	www.newton.cam.ac.uk /reports/0203/nst.html (2154 words)

	Weight One Motivic Cohomology and (ResearchIndex)
		The computations show that the homotopy groups of the weight one piece coincides with the weight one motivic cohomology groups, thus providing evidence that the filtration is correct.
		Motivic complexes and the K-theory of automorphisms - Walker (1997)
		Weight Zero Motivic Cohomology and the General Linear Group of a..
	citeseer.ist.psu.edu /302838.html (195 words)

	Motivic cohomology and algebraic cycles a categorical approach, by Marc Levine
		For S a field of characteristic zero, or a smooth curve over a field of characteristic zero, the motivic cohomology agrees with Bloch's higher Chow groups; the same is true in characteristic p>0 if one uses Q-coefficients.
		In particular, the motivic cohomology agrees rationally with the weight-graded pieces of algebraic K-theory, for S smooth and of dimension at most one over a field.
		In addition, each reasonable graded cohomology theory Gamma(*) on the category of smooth, quasi-projective schemes over a fixed base S gives rise to a realization functor Re_Gamma for DM(S); for example, we have the Betti, e'tale and Hodge realizations of DM(S).
	www.math.uiuc.edu /K-theory/0107/index.html (202 words)

	preprints
		A short course on geometric motivic integration, These notes grew out of my effort to understand the theory of motivic integration and are based on several introductory lectures I gave during 2002-2005.
		We show that the localization of a regular ring R of positive characteristic at a single element $f$ is generated, as a $D$-module, by $f^{-1}$ This is in contrast to the situation in characteristic zero where the $D$-generation is goverened by the zeros of the Bernstein-Sato polynomial.
		Local cohomology multiplicities in terms of étale cohomology, with Raphael Bondu (to appear in Ann Inst Fourier).
	www.mabli.org /preprints.html (598 words)

	Amazon.fr : Cycles, Transfers, and Motivic Homology Theories: Livres: Vladimir Voevodsky,Andrei Suslin,Eric M. ... (Site not responding. Last check: 2007-09-30)
		The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum.
		The Friedlander-Lawson moving lemma for families of algebraic cycles appears in the third paper in which a bivariant theory called bivariant cycle cohomology is constructed.
		The fifth and last paper in the volume gives a proof of the fact that bivariant cycle cohomology groups are canonically isomorphic (in appropriate cases) to Bloch's higher Chow groups, thereby providing a link between the authors' theory and Bloch's original approach to motivic (co-)homology.
	www.amazon.fr /exec/obidos/ASIN/0691048150 (353 words)

	[No title]
		Since in this * case computing 'etale cohomology* involves exactly the same steps as computing motivic cohomology, we have gone ahead and computed the stronger invariant (to be used in future work).
		Fina* lly, the cohomology* groups of the quadrics are both isomorphic to Mi-1,02, and the m* *ap between them is also the identity.
		[SV] A. Suslin and V. Voevodsky, Bloch-Kato conjecture and motivic cohomology w* ith finite coefficients, in The arithmetic and geometry of algebraic cycles (Banff, A *B, 1998), NATO Sci.
	www.math.purdue.edu /research/atopology/Dugger-Isaksen/hopfDI.txt (5428 words)

	Research
		One of the things I study is motivic homotopy theory, which is a blend of homotopy theory and algebraic geometry.
		The basic idea is to replace techniques involving cohomology theories for topological spaces with techniques involving algebraic cohomology theories.
		One of the motivations is that motivic homotopy theory is a subject that is in need of more computations.
	www.math.wayne.edu /~isaksen/Research (1347 words)

	Abel-Jacobi mappings and finiteness of motivic cohomology groups, Kanetomo Sato
		[36]\bibitem [K3]k1 —, ``Semi-stable reduction and $p$-adic étale cohomology'' in Périodes $p$-adiques (Bures-sur-Yvette, 1988), Astérisque 223, Soc.
		[42]\bibitem [Le2]levine:mot —, $K$-theory and motivic cohomology of schemes, preprint, 1999.
		[59]\bibitem [SuVo]sv:bk A. Suslin and V. Voevodsky, Bloch-Kato conjecture and motivic cohomology with finite coefficients, preprint, 1999.
	projecteuclid.org /getRecord?id=euclid.dmj/1092403652 (1128 words)

	motivic course (Site not responding. Last check: 2007-09-30)
		Abstract: In these lectures, we will describe Voevodsky's construction of Motivic Cohomology for smooth algebraic varieties and his derived category of motives, and explain their basic properties.
		Lecture 1: Topological motivation; background material in homological algebra and category theory.
		Lectures in Motivic Cohomology (notes by C.Weibel and C.Mazza).
	www.math.ist.utl.pt /~pedfs/motivic_course.html (137 words)

	Weight one motivic cohomology and K-theory - Walker (ResearchIndex)
		K-Theory And Motivic Cohomology Of Schemes - Levine
		3: Motivic Complexes and the K-theory of Automorphisms - Walker - 1996
		22 A spectral sequence for motivic cohomology - Bloch, Lichtebaum
	citeseer.ist.psu.edu /250277.html (465 words)

	Motives - (American Mathematical Society Bookstore) (Site not responding. Last check: 2007-09-30)
		Motives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field.
		A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.
		Cohomology S. Kleiman -- The standard conjectures N. Katz -- Review of $\ell$-adic cohomology J. Steenbrink -- A summary of mixed Hodge theory L. Illusie -- Crystalline cohomology J. Tate -- Conjectures on algebraic cycles in $\ell$-adic cohomology
	mirror.math.nankai.edu.cn /mirror/www.ams.org/PSPUM-55.html (963 words)

	Citebase - Karoubi's Construction for Motivic Cohomology Operations
		We use an analogue of Karoubi's construction in the motivic situation to give some cohomology operations in motivic cohomology.
		We prove many properties of these operations, and we show that they coincide, up to some nonzero constants, with the reduced power operations in motivic cohomology originally constructed by Voevodsky.
		The relation of our construction to Voevodsky's is, roughly speaking, that of a fixed point set to its associated homotopy fixed point set.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0603458 (133 words)

	motivic - OneLook Dictionary Search
		We found 4 dictionaries with English definitions that include the word motivic:
		Tip: Click on the first link on a line below to go directly to a page where "motivic" is defined.
		motivic : The American Heritage® Dictionary of the English Language [home, info]
	www.onelook.com /?w=motivic (140 words)

	Matches for:
		This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions.
		The author constructs and describes a triangulated category of mixed motives over an arbitrary base scheme.
		Most of the classical constructions of cohomology are described in the motivic setting, including Chern classes from higher $K$-theory, push-forward for proper maps, Riemann-Roch, duality, as well as an associated motivic homology, Borel-Moore homology and cohomology with compact supports.
	www.mathaware.org /bookstore?fn=20&arg1=survseries&item=SURV-57-E (151 words)

	Milne: Motivic cohomology and values of zeta functions
		Milne: Motivic cohomology and values of zeta functions
		Milne, J. Motivic cohomology and values of zeta functions.
		: Duality in the flat cohomology of a surface, Ann.
	www.numdam.org /numdam-bin/item?id=CM_1988__68_1_59_0 (338 words)

	Atlas: Finiteness results for certain motivic cohomology groups by Uwe Jannsen (Site not responding. Last check: 2007-09-30)
		This is a report on joint work in progress with Shuji Saito.
		We prove finiteness for certain motivic cohomology groups modulo n, viz., the groups CH
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqo-85.
	atlas-conferences.com /cgi-bin/abstract/caqo-85 (212 words)

	Notes on motivic cohomology, A. Beilinson, R. MacPherson, V. Schechtman
		Notes on motivic cohomology, A. Beilinson, R. MacPherson, V. Schechtman
		[B3] A. Beilinson, Notes on absolute Hodge cohomology, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), Contemp.
		[K] F. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, vol.
	projecteuclid.org /getRecord?id=euclid.dmj/1077305678 (447 words)

	USC College: Faculty: Department of Mathematics: Thomas Geisser (Site not responding. Last check: 2007-09-30)
		Professor Geisser studies arithmetic algebraic geometry, algebraic K-theory, and motivic cohomology.
		Geisser, T. (2004) "Motivic Cohomology over Dedekind rings" Mathematische Zeitschrift, Vol.
		Geisser, T. (2005) "Motivic cohomology, algebraic K-theory and topological cyclic" in Friedlander, Grayson (Eds.) Handbook of K-theory, Springer pp.193-234
	usc.edu /assets/college/faculty/profiles/236.html>ThomasGeisser</... (265 words)

	Voevodsky, V., Suslin, A., Friedlander, E.M.: Cycles, Transfers, and Motivic Homology Theories. (AM-143).
		Voevodsky, V., Suslin, A., Friedlander, E.M.: Cycles, Transfers, and Motivic Homology Theories.
		Chapter 4 Bivariant Cycle Cohomology Eric M. Friedlander and Vladimir Voevodsky 138
		Chapter 6 Higher Chow Groups and Etale Cohomology Andrei A. Suslin 239
	pup.princeton.edu /titles/7003.html (314 words)

	Mathematics Archives - Topics in Mathematics - Abstract Algebra
		Graduate courses on Group Theory, Fields and Galois Theory, Algebraic Number Theory, Class Field Theory, Modular Functions and Modular Forms, Elliptic Curves, Algebraic Geometry, Lectures on Etale Cohomology, Abelian Varieties
		Course Notes, Group Theory, Fields and Galois Theory, Algebraic Geometry, Algebraic Number Theory, Modular Functions and Modular Forms, Elliptic Curves, Abelian Varieties, Lectures on Etale Cohomology, Class Field Theory, Preprints
		Notes on Algebraic Geometry, Étale Cohomology, Algebraic Surfaces, Curves on Surfaces
	archives.math.utk.edu /topics/abstractAlgebra.html (1342 words)

Try your search on: Qwika (all wikis)