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Topic: Weight monodromy conjecture

	Weight-monodromy conjecture for certain threefolds in mixed characteristic (Site not responding. Last check: 2007-09-18)
		Weight-monodromy conjecture for certain threefolds in mixed characteristic
		The aim of this paper is to give a proof of the weight-monodromy conjecture for a threefold which has a projective strictly semistable model such that, for each irreducible component of the special fiber, the Picard number is equal to the second
		-adic analogue by using the weight spectral sequence of Mokrane.
	www.hindawi.com /GetArticle.aspx?doi=10.1155/S1073792804130250 (187 words)

	[No title]
		What I termed the ``Shimura-Taniyama-Weil'' conjecture became known as the ``modular curve conjecture'' and then, from the summer of 1999, as the ``modular curve theorem'' after the work of Breuil, Conrad, Diamond, and Taylor in the same vein as the work of Wiles and Taylor for the ``semi-stable'' case.
		This conjecture, even as a conjecture, has served as an important motivating example for the idea of the ``Langlands Program'', or perhaps of an extension of that program, that certain kinds of objects in geometry should give rise to certain group representations.
		The conjecture states that the L-function of an elliptic curve defined over $\Q$ with conductor $N$ arises from a cuspform for the group $\Gamma_0(N)$ that is compatible with the substitution in the upper-half plane $H$ given by $W_N$\@.
	www.albany.edu /~hammond/gellmu/examples/f356g.glm (5880 words)

	Algebraic Number Theory Archive (Site not responding. Last check: 2007-09-18)
		ANT-0342: 28 Mar 2002, On an Archimedean analogue of Tate's conjecture, by Dipendra Prasad and C.S.Rajan.
		ANT-0185: 7 Jun 1999, An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod-p cohomology of GL(n,Z), by Avner Ash and Warren Sinnott.
		ANT-0130: 31 Aug 1998, Counterexamples to a conjecture of Lemmermeyer, by Nigel Boston and Charles Leedham-Green.
	front.math.ucdavis.edu /ANT (12251 words)

	List of conjectures - Wikipedia, the free encyclopedia
		Erdős conjecture, which lists conjectures of Paul Erdős and his collaborators
		Blattner's conjecture (now often known as the Blattner formula)
		Epsilon conjecture (an intermediate on the way to Fermat's last theorem)
	en.wikipedia.org /wiki/List_of_conjectures (126 words)

	Fields Institute - Workshop on Shimura varieties and related topics
		Conjecturally the Zariski closure of the orbits of the Hecke symmetries are exactly the closures of ``leaves'' in Oort's foliation.
		This applies to a conjecture of Prasad on autodual representations of division algebras.
		The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply an argument of Steenbrink, M. Saito to the weight spectral sequence of Rapoport-Zink.
	www.fields.utoronto.ca /programs/scientific/02-03/automorphic_forms/shimura/abstracts.html (1764 words)

	Fellowship of the Ring Seminar
		We specify a set of weights, determined by the restriction of \rho to the inertia subgroup at P, which contains all the weights for which \rho is modular (and, conjecturally, nothing else; we have partial results in this "converse" direction).
		These conjectures are much more precise in the case of abelian extensions, and over the years a number of generalizations and/or refinements have been made.
		Abstract: Recent conjecture of Kontsevich-Soibelman and Gross-Wilson asserts that the Gromov-Hausdorff limit of a maximally degenerate Calabi-Yau family is a sphere with Monge-Ampere Kahler affine structure with singularities in codimension 2.
	people.brandeis.edu /~fdiamond/pastfor.html (6881 words)

	Modular Abelian Varieties
		Let M be a space of weight 2 cuspidal modular symbols with trivial character that corresponds to a Galois-conjugacy class of newforms, and let A_M(C) be the cokernel of the period map.
		Let M be a space of modular symbols of weight 2 and trivial character.
		Modular symbols space of level 54, weight 2, and dimension 4 > qE := qIntegralBasis(E,17); > qA54 := qIntegralBasis(A54,17); > and+qA54 - and+qE; -3q^4 + 3q^5 - 3q^8 + 3q^10 - 3q^11 + 9q^13 + 3*q^16 + O(q^17) > IntersectionGroup(E,A54); // however, the intersection is trivial.
	www.umich.edu /~gpcc/scs/magma/text1113.htm (1087 words)

	[No title]
		An old conjecture holds that the number N_n(X) of degree n number fields with discriminant less than X is asymptotic to c_n X when X grows and n is fixed.
		There's a slight wrinkle: the weight 1 Hilbert modular form f attached to E[3] by Langlands-Tunnell might not be ordinary, and thus one cannot necessarily find a higher-weight modular lift of E[3] whose restriction to decomposition groups at 3 we can control.
		We give an example showing two dessins with the same monodromy group and local ramification data which are separated by the braid group invariant.
	www.math.princeton.edu /~ellenber/papers.html (1955 words)

	McMaster's Algebra/Number Theory Seminar
		Modular forms of half-integral weight are more difficult to deal with, but Shimura proved a nice correspondence from these forms to modular forms of integral weight.
		In the early 70's Serre conjectured a converse to this, that is, given a mod $p$ 2 dimensional representation of
		In this talk, I will describe one of these conjectures in some detail, illustrating it in some cases where it is known, and explain some of my work towards proving it in the case when the variety is a self-product of the Fermat curve, $${\mathbf F_N}: X^{N}+Y^{N}+Z^{N}=0$$.
	www.math.mcmaster.ca /talks/algebra_number_theory/abstracts.html (2129 words)

	Stony Brook Math Calendar
		Its monodromy gives a one-parameter family of representations of the generalised braid group Bg of type g which deforms the action of (a finite extension of) the Weyl group of g on V.
		The Seifert conjecture is the assertion that a smooth nonvanishing vector field on the three sphere must have a closed trajectory.
		The Seifert conjecture is the question, posed by Seifert (1950), whether or not every smooth non-vanishing vector field on the 3-dimensional sphere has a periodic orbit.
	www.math.sunysb.edu /~calendar/scott.php?LocationID=&Date=2003-03-01 (5495 words)

	Abstract (Site not responding. Last check: 2007-09-18)
		In this talk, I will give a proof of the weight-monodromy conjecture (Deligne's conjecture on the purity of monodromy filtration) for varieties with p-adic uniformization by the Drinfeld upper half spaces of any dimension.
		The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply an argument of Steenbrink, M. Saito to the weight spectral sequence of Rapoport-Zink.
		As an application, by combining this result with the results of Schneider-Stuhler, we compute the local zeta functions of p-adically uniformized varieties in terms of representation theoretic invariants.
	www.uni-regensburg.de /Fakultaeten/nat_Fak_I/aktuelles/zusaetze/itoabstract.htm (115 words)

	The Distribution of the Eigenvalues of Hecke Operators (ResearchIndex) (Site not responding. Last check: 2007-09-18)
		For each prime p, we determine the distribution of the p th Fourier coefficients of the Hecke eigenforms of large weight for the full modular group.
		Introduction and statement of results Let f(z) = 1 X n=1 a f;n e(nz) be a cusp form of weight k for the full modular group.
		We assume that f(z) is an eigenfunction of all the Hecke operators T n, and we set a f (n) = n 1\Gammak 2 a f;n.
	sherry.ifi.unizh.ch /159341.html (368 words)

	[No title]
		\ What I termed the ``Shimura-Taniyama-Weil'' conjecture became known as the ``modular curve conjecture'' and then, from the summer of 1999, as the ``modular curve theorem'' after the work of Breuil, Conrad, Diamond, and Taylor in the same vein as the work of Wiles and Taylor for the ``semi-stable'' case.
		Weil (\cite{weilmathann}) showed that the cuspforms of weight \(2\) for the group \(\Gamma{}_{0}(N)\) satisfying the appropriate functional equation under the mapping of \(H\) given by \(W_{N}\) correspond precisely to Dirichlet series with certain growth conditions that admit analytic continuations as meromorphic functions in \(\mbox{\textbf{C}}\) satisfying a finite number of ``twisted'' functional equations.
		\ The conjecture states that the L-function of an elliptic curve defined over \(\mbox{\textbf{Q}}\) with conductor \(N\) arises from a cuspform for the group \(\Gamma{}_{0}(N)\) that is compatible with the substitution in the upper-half plane \(H\) given by \(W_{N}\)\@.
	www.albany.edu /~hammond/gellmu/examples/f356g.ltx (5370 words)

	On the -adic -function of a modular form at a supersingular prime, Robert Pollack
		When $a\sb p=0$, we are able to decompose both the sum and the difference of the two unbounded distributions attached to $f$ into a bounded measure and a distribution that accounts for all of the growth.
		Moreover, we interpret Kurihara's conjectures on the Galois structure of the Tate-Shafarevich group in terms of these two Iwasawa functions.
		[8] R. Greenberg and G. Stevens, ``On the conjecture of Mazur, Tate, and Teitelbaum'' in $p$-adic Monodromy and the Birch and Swinnerton-Dyer Conjecture (Boston, 1991), Contemp.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.dmj/1082744678 (712 words)

	Anarawd ap Gruffydd (Site not responding. Last check: 2007-09-18)
		The Deligne conjecture on special values of L-function s is a formulation of the general hopes for formulae in closed term s 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 motive (algebraic geometry) in algebraic geometry.
		There is Deligne conjecture in the representation theory of the exceptional Lie group s.
	anarawd.ap.gruffydd.en.reee.org (4961 words)

	[No title]
		In a recent paper, Calegari and Dunfield exhibit a sequence of hyperbolic 3-manifolds which have increasing injectivity radius, and which, subject to some conjectures in number theory, are rational homology spheres.
		We prove unconditionally that these manifolds are rational homology spheres, and give a sufficient condition for a tower of hyperbolic 3-manifolds to have first Betti number 0 at each level.
		This conjecture was proved by Davenport and Heilbronn for n = 3, and recently for n = 4,5 by Bhargava.
	math.wisc.edu /~ellenber/papers.html (2312 words)

	The 23 Paris Problems
		Max Dehn, one of the founders of topology, confirmed Hilbert's conjecture in 1900, the same year the problem was first posed.
		Hence, Hilbert optimistically conjectured that all such subrings are finitely generated.
		He further conjectured that snowflakes take on hexagonal shapes because the "tightest pack" is that of a face-centered cubic lattice.
	www.math.umn.edu /~wittman/problems2.html (2827 words)

	Search Results for theorem
		The theorem was conjectured in the 18th century, Chebyshev himself came close to a proof, but it was not proved until 1896, when Hadamard and de la Vallee Poussin independently proved it using complex analysis.
		This theorem was conjectured in the 18th century, but it was not proved until 1896, when Hadamard and (independently) Charles de la Vallee Poussin, used complex analysis.
		This conjecture proved to be a major factor in the proof of Fermat's Last Theorem by Wiles.
	www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=theorem&CONTEXT=1 (15689 words)

	Modular abelian varieties (Site not responding. Last check: 2007-09-18)
		Let M be a space of weight 2 cuspidal modular symbols with trivial character, which is the kernel of an ideal in the Hecke algebra.
		We assume that M has weight two and trivial character; the modular degree of M is then the square root of the order of ModularKernel(M).
		The real and minus Tamagawa numbers are defined even for higher weight spaces of modular symbols over the rationals.
	www.sci.kuniv.edu.kw /magma/text799.html (995 words)

	Citations: Good reduction of abelian varieties - Serre, Tate (ResearchIndex)
		To state more results on Conjecture 0.3, we recall the monodromy filtration and the weight monodromy conjecture.
		Appendix, there exist a nilpotent endomorphism N (X K, Q #) 1) and an open subgroup J I K such that, for # J, the action of # on H (X K, Q #) is given by exp(t # (#)N) Let M.
		Serre's Conjecture on 2-dimensional Galois Representations - Charles
	citeseer.ist.psu.edu /context/635690/0 (1918 words)

	Weight Spectral Sequences and Independence of l (ResearchIndex)
		Abstract: this paper, we establish the necessary basic properties, Corollaries 1.17, 1.20, 1.22, 1.24, Proposition 1.26 etc. of weight spectral sequences such as functoriality, compatibility with the product with algebraic cycles, the push-forward, the duality, algebraic correspondences etc. We derive them from a formal construction, Corollary 1.12, of the weight spectral sequences.
		It is known that the construction of the weight spectral sequence follows from an identification of the graded pieces of...
		2 Monodromy weight filtration is independent of l (context) - Terasoma
	citeseer.ist.psu.edu /472524.html (458 words)

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