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Topic: Deligne conjecture


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In the News (Fri 24 May 19)

  
  Pierre Deligne - Wikipedia, the free encyclopedia
Pierre Deligne (born 3 October 1944) is a Belgian mathematician.
From 1970 until 1984, when he moved to the Institute for Advanced Study in Princeton, Deligne was a permanent member of the IHES staff.
During this time he did much important work, besides the proof of the Weil conjectures: in particular with George Lusztig on the use of ├ętale cohomology to construct representations of algebraic groups, and with Rapoport on the moduli spaces from the 'fine' arithmetic point of view, with application to modular forms.
en.wikipedia.org /wiki/Pierre_Deligne   (367 words)

  
 Deligne conjecture - Wikipedia, the free encyclopedia
The Deligne conjecture on special values of L-functions is a formulation of the general hopes for formulae in closed terms for L(n) where L is an L-function and n an integer.
There is a Deligne conjecture on 1-motives arising in the theory of motives in algebraic geometry.
There is a Deligne conjecture on monodromy, also known as the weight monodromy conjecture, or purity conjecture for the monodromy filtration.
en.wikipedia.org /wiki/Deligne_conjecture   (192 words)

  
 Search Results for conjecture*
This conjecture became known as "the main conjecture on cyclotomic fields" and it remained one of the most outstanding conjectures in algebraic number theory until it was solved by Mazur and Wiles in 1984 using modular curves.
Burnside conjectured that every finite group of odd order is soluble and it is not surprising that he failed to prove this result as it was not proved until 1962 when W Feit and J C Thompson proved the result in a 300 page paper.
In 1973 it had been conjectured that the behaviour of the logistic equation was the same in a qualitative sense for all g(x) which have a maximum value and decrease monotonically on either side of this maximum.
www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=conjecture*&CONTEXT=1   (9425 words)

  
 [No title]   (Site not responding. Last check: 2007-08-08)
The significance of the project on Deligne's Conjecture consists in studying presumably deep connections between one complex variable and associative algebras.
Deligne's Conjecture may be reformulated as the existence of a certain string theory associated to every associative algebra.
The significance of the moduli space part of the project is in extending the fundamental relationship between the geometry of a homogeneous space and the representation theory of a semisimple Lie group to the case of the moduli space of Riemann surfaces and the Virasoro algebra, respectively.
www.cs.utexas.edu /users/yguan/NSFAbstracts/Abstracts/MPS/DMS.MPS.a9971434.txt   (436 words)

  
 Pierre Deligne   (Site not responding. Last check: 2007-08-08)
During this time he did much important work, besides the proof of the Weil conjectures: in particular with Lusztig on the use of etale cohomology to construct representations of algebraic groups, and with Rapoport on the moduli spaces from the 'fine' arithmetic point of view.
In terms of the completion of some of the underlying Grothendieck programme of research, he defined absolute Hodge cycles, as a surrogate for the missing and still largely conjectural theory of motives.
Deligne has written a book with G.D. Mostow on monodromy.
www.worldhistory.com /wiki/P/Pierre-Deligne.htm   (422 words)

  
 Deligne's conjecture on 1-motives, L. Barbieri-Viale, A. Rosenschon, M. Saito   (Site not responding. Last check: 2007-08-08)
Deligne's conjecture on 1-motives, L. Barbieri-Viale, A. Rosenschon, M. Saito
We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soulé on cohomology, and prove it.
If the degree of cohomology is at most two, we can prove the conjecture for the Hodge realization without isogeny, and even for 1-motives with torsion.
projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.annm/1069786255   (67 words)

  
 [No title]
They include a few more geometric versions of Deligne's conjecture (as compared to the original Tamarkin version) by McClure and Smith, Kontsevich and Soibelman, and the reviewer, and further simplification (by Tamarkin and Tsygan) of Tamarkin's proof of the deformation quantization theorem, using Etingof-Kazhdan "dequantization" rather than quantization.
They include a few more geometric versions of Deligne's conjecture (as compared to the original Tamarkin version [math.QA/9803025]) by McClure and Smith [math.QA/9910126], Kontsevich and Soibelman [math.QA/0001151], and the reviewer [math.QA/9807037], and further simplification [math.KT/0002116] (by Tamarkin and Tsygan) of Tamarkin's proof of the deformation quantization theorem [math.QA/9803025], using Etingof-Kazhdan "dequantization" [q-alg/9701038] rather than quantization.
In 1994 E. Getzler and J. Jones posted on the e-print server a preprint [hep-th/9403055] in which the proof of the Deligne conjecture was contained.
www.math.niu.edu /~rusin/known-math/00_incoming/featured   (793 words)

  
 -functions   (Site not responding. Last check: 2007-08-08)
In joint work with Freydoon Shahidi, I want to prove Deligne's conjectures on the special values of the symmetric fourth power
This conjecture has a motivic framework but can be formulated purely in the automorphic context.
Mahnkopf's approach is an inductive approach and there are many issues to settle before one can use his results.
www.math.uiowa.edu /~araghura/research/node6.html   (170 words)

  
 Citations: La conjecture de Weil - Deligne (ResearchIndex)   (Site not responding. Last check: 2007-08-08)
In fact, Ramanujan only made his conjecture for (n) and the general conjecture for cusp forms for congruence subgroups was made by Petersson, so this is now called the Ramanujan Petersson conjecture.
Deligne s bound was later applied by Phillips and Sarnak to graph theory in the construction of explicit expanders [69] For more information about representation of integers as sums of squares, see the survey article of W. Duke [22] A more....
This together with Grothendieck s rationality theorem shows that the archimedian Dwork conjecture is indeed true in the geometric case, but still open in general and depends on Deligne s conjecture.
citeseer.ist.psu.edu /context/56162/0   (2373 words)

  
 A solution of Deligne's conjecture. - McClure, Smith (ResearchIndex)   (Site not responding. Last check: 2007-08-08)
Abstract: Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad.
The reason for the amnesia is that, to define Steenrod operations in mod p cohomology for odd primes p, the higher homotopies were...
0.3: A Counterexample to a Conjecture of Barr - Whitehouse (1996)
citeseer.ist.psu.edu /mcclure99solution.html   (562 words)

  
 Homotopical algebra and higher categories
The main motivation for the theory is Simpson's weak-unit conjecture according to which $n$-groupoids with strict composition laws and weak units should model all homotopy $n$-types.
A proof of this conjecture in dimension $3$ is announced, obtained in joint work with A.~Joyal.
This implies a version of Simpson's weak-unit conjecture in dimension $3$, namely that one-object $3$-groupoids that are strict in all respects, except that the object has only weak identity arrows, can model all connected, simply connected homotopy types.
mat.uab.es /~kock/cat.html   (776 words)

  
 [No title]
In this case, the Gerstenhaber algebra structure in homology is a c* *onsequence of the action of the little 2-cubes operad C2 on 2A.
In 1993, Deligne [6] ask* *ed whether there was a closer relation between these two examples: specifically, he asked * *whether the Gerstenhaber algebra structure of H*(R) is induced by an action on C*(R) of a c* *hain operad quasi-isomorphic to the singular chain operad of C2.
This is usually known as * *Deligne's conjecture, although in the original letter it was expressed as a desire or pre* *ference ("I would like the complex computing Hochschild cohomology to be an algebra over [the sin* *gular chain operad of the little 2-cubes] or a suitable version of it").
hopf.math.purdue.edu /McClure-SmithJH/deligne_conj.txt   (10208 words)

  
 A99shoi.html   (Site not responding. Last check: 2007-08-08)
Formality theorem, Kontsevich's theorem on complex manifold, and Deligne conjecture on 3-valent graphs
the statement and the proof of Deligne conjecture on 3-valent graphs, as well as its odd analog, and cohomological generalizations of both theorems;
general conjecture "Duflo formula for Q-manifolds", which is a generalization of both Duflo theorem and the theorem on complex manifold--it is based on the notion of Atiyah class in Lie algebra cohomology.
www.math.univ-montp2.fr /GTA/A99shoi.html   (102 words)

  
 [No title]   (Site not responding. Last check: 2007-08-08)
Martin Markl Mathematical Institute of the Academy of Science, Prague Topic: Variations on the Deligne Conjecture Date: Thursday, October 28, 2004 Place: Room 614 of the Science & Education Building, Univ. of Haifa Time: 12:10 Note: This will also be an organizational meeting for the seminar for this semester.
Abstract: One of the formulations of the Deligne conjecture states the existence of a natural action of a chain version of the little discs operad on the Hochschild cochain complex of an associative algebra.
This conjecture, which certainly does not sound very attractive, has many interesting and surprizing applications, for example in Kontsevich's formality theorem.
www.math.technion.ac.il /~techm/20041028121020041028mar   (200 words)

  
 ABSTRACTS   (Site not responding. Last check: 2007-08-08)
It is not quite clear why Deligne conjectured a few years ago that there must be a deep connection between the little disks operad and the Hochschild complex, but it turned out to be not only true, but far from being trivial and have powerful applications to deformation theory.
In this talk we will attempt to explain Deligne's Conjecture from the point of view of the topology of the little disks operad and moduli spaces of punctured Riemann spheres.
Finally, we will indicate how these decompositions may actually be related to the decompositions of the Taylor tower of some functors into a product of their layers, and how this leads to a generalizations of the results.
www.math.uchicago.edu /~mandell/seminar/abstracts-200001.html   (181 words)

  
 Workshop on Noncommutative Geometry and Number Theory
There are well known relations of Hochschild homology and cyclic homology of the chains on a space and the loop space to the Homology of the free loop space.
Using these results we conjecture that there an extension of string topology, which essentially is given by the framed little discs operad, with operations coming from all of moduli space and from all genera.
In the course of constructing a proof of the Baum-Connes conjecture for p-adic GL(n), Baum-Higson-myself had to compute the periodic cyclic homology of the affine Hecke algebra H(n,q).
www.mpim-bonn.mpg.de /html/services/activities/noncom_2004_abstracts.html   (1623 words)

  
 Bibliography   (Site not responding. Last check: 2007-08-08)
S. Bloch and A. Ogus, Gersten's conjecture and the homology of schemes, Ann.
P. Deligne, La Conjecture de Weil pour les surfaces K3, Inventiones Math.
P. Deligne, J. Milne, A. Ogus, K.-Y. Shih, Hodge Cycles, Motives and Shimura Varieties, Springer-Verlag LNM 900, 2nd ed.
www.imsc.ernet.in /~kapil/work/node16.html   (248 words)

  
 [No title]   (Site not responding. Last check: 2007-08-08)
Abstract: One of the formulations of the Deligne conjecture affirms the existence of a natural action of a chain version of the little discs operad on the Hochschild cochain complex of an associative algebra.
This conjecture has many interesting and surprizing applications, for example in Kontsevich's formality theorem.
I will sketch a proof of this conjecture proposed by Tamarkin, that uses the quantization procedure by Etingof and Kazhdan.
www.cs.biu.ac.il /~katzmik/colloquium/markl.html   (131 words)

  
 Bulletin of the American Mathematical Society
E. Freitag and R. Kiehl, Etale Cohomology and the Weil conjecture, Springer-Verlag, 1988.
D. Gaitsgory, On a vanishing conjecture appearing in the geometric Langlands correspondence, Preprint math.AG/0204081.
G. Laumon, Transformation de Fourier, constantes d'équations fonctionelles et conjecture de Weil, Publ.
www.ams.org /bull/2004-41-02/S0273-0979-04-01001-8/home.html   (769 words)

  
 philadelphia.ca - conjecture guess   (Site not responding. Last check: 2007-08-08)
We couldn't find any results for conjecture guess in Books.
Here are some other items you may be interested in.
forums and see all kinds of conjecture and speculation as to what Google was doing.
philadelphia.ca /conjecture-guess/reference/search   (363 words)

  
 AMS Summer 1999 Research Conference in Algebraic Topology Abstracts   (Site not responding. Last check: 2007-08-08)
This talk is based on joint work with Charles Rezk and Stefan Schwede.
Deligne conjectured that the little two cubes operad acts on the Hochschild complex of a DGA.
In joint work McClure and Smith prove a generalization: If a cosimplicial object (the objects can be spaces or spectra or DG modules) has a cup product and "circle i" products then its Tot has an action of the little two cubes operad.
www.math.wayne.edu /~rrb/Summer99/abstracts6.html   (439 words)

  
 WEB :: Algebraic Geometry
A description of the conjecture by Deligne (PDF) and details of the prize offered for its resolution.
Short introductory sketch of some topics in the algebraic geometry of curves.
Aims to answer the basic questions this theory B(n,d,k) for vector bundles on algebraic curves.
www.categoryweb.com /Top/Science/Math/Geometry/Algebraic_Geometry   (44 words)

  
 Crystalline realizations of 1-motives, by F. Andreatta and L. Barbieri Viale   (Site not responding. Last check: 2007-08-08)
We consider the crystalline realization of Deligne's 1-motives in positive characteristics and prove a comparison theorem with the De Rham realization of liftings to zero characteristic.
We then show that one dimensional crystalline cohomology of an algebraic variety, defined by universal cohomological descent via de Jong's alterations, coincide with the crystalline realization of the Picard 1-motive, over perfect fields.
L. Barbieri Viale, A. Rosenschon & M. Saito: Deligne's conjecture on 1-motives, to appear on Annals of Math (Princeton, USA).
www.math.uiuc.edu /K-theory/0620   (158 words)

  
 Journal of the American Mathematical Society
In this paper we derive the geometric Langlands conjecture from a certain vanishing conjecture.
Furthermore, using recent results of Lafforgue, we prove this vanishing conjecture, and hence the geometric Langlands conjecture, in the case when the ground field is finite.
P. Deligne, La conjecture de Weil II, Publ.
www.ams.org /jams/2002-15-02/S0894-0347-01-00388-5/home.html   (551 words)

  
 Ellen And Jim Have A Blog, Too: Math
We illustrate the diversity of the area with a deep conjecture that stands as a very special case of various dimensional conjectures we make below and provide evidence for:
Perhaps only mathematicians will get the joke about a conjecture by Deligne about an object defined by Grothendieck being a special case of something wider.
It is the only use of the word algebra in this sense, while the words field and ring make no appearance at all in either volume.
server4.moody.cx /?c=Math   (680 words)

  
 Proceedings of the American Mathematical Society   (Site not responding. Last check: 2007-08-08)
(this last assumption is unnecessary if the semisimplicity conjecture is true).
This verifies a conjecture of Grothendieck and Serre provided the semisimplicity conjecture holds.
The proof relies heavily on Deligne's work on Weil conjectures.
0-www.ams.org.library.uor.edu /proc/1999-127-09/S0002-9939-99-05414-3/home.html   (212 words)

  
 [No title]
Shrawan Kumar, Towards a proof of the Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras.
Mike Keane, On spontaneous emergence of opinions: Results and conjectures concerning reinforced random walks.
Kobi Peterzil, On Pillay's Group Conjecture for o-minimal structures.
www.math.technion.ac.il /~techm/tmoldmsg.html   (7687 words)

  
 Geometry - Webalcance.com   (Site not responding. Last check: 2007-08-08)
Differential Algebraic Geometry - A Scheme-theoretic Approach - Slides in multimedia format from a lecture by Henri Gillet at MSRI.
The Hodge Conjecture - A description of the conjecture by Deligne (PDF) and details of the prize offered for its resolution.
Introduction to Algebraic Geometry - Illustrated webnotes by Donu Arapura.
www.webalcance.com /directory/cat.asp?/Science/Math/Geometry/Algebraic_Geometry   (157 words)

  
 List of Publications of Ralph M. Kaufmann
Kaufmann, Ralph M. "On Spineless Cacti, Deligne's Conjecture and Connes-Kreimer's Hopf Algebra.''
Kaufmann, Ralph M. "A proof of a cyclic version of Deligne's conjecture via Cacti"
Kaufmann, Ralph M. "Arcs, Ribbons, Moduli spaces and applications to Deligne's conjecture''
www.math.uconn.edu /~kaufmann/pubs.html   (260 words)

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