2009

最新文章

• Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces AI翻译
  作者：Hacking, Paul; Keel, Sean; Tevelev, Jenia
  作者单位：University of Washington; University of Washington Seattle; University of Texas System; University of Texas Austin; University of Massachusetts System; University of Massachusetts Amherst
  摘要：We give a functorial normal crossing compactification of the moduli space of smooth cubic surfaces entirely analogous to the Grothendieck-Knudsen compactification M-0,M-n subset of (M-0,M-n) over bar.
• Serre's modularity conjecture (II) AI翻译
  作者：Khare, Chandrashekhar; Wintenberger, Jean-Pierre
  作者单位：Utah System of Higher Education; University of Utah; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
  摘要：We provide proofs of Theorems 4.1 and 5.1 of Khare and Wintenberger (Invent. Math., doi: 10.1007/s00222-009-0205-7, 2009).
• Faltings heights of CM cycles and derivatives of L-functions AI翻译
  作者：Bruinier, Jan Hendrik; Yang, Tonghai
  作者单位：Technical University of Darmstadt; University of Wisconsin System; University of Wisconsin Madison
  摘要：We study the Faltings height pairing of arithmetic special divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedean contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a Rankin L-function. We prove the conjecture in certain cases where the Shimura variety has dimension 0, 1, or 2. In particular, we obtain a new proof of the Gross-Zagier formula.
• The hypertoric intersection cohomology ring AI翻译
  作者：Braden, Tom; Proudfoot, Nicholas
  作者单位：University of Massachusetts System; University of Massachusetts Amherst; University of Oregon
  摘要：We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category. The computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice...
• On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory AI翻译
  作者：Panin, Ivan; Pimenov, Konstantin; Roendigs, Oliver
  作者单位：University of Bielefeld; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; University Osnabruck
  摘要：Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P-1-spectrum MGL of Voevodsky is considered as a commutative P-1-ring spectrum. Setting MGL(i) = circle plus(p-2q=i) MGL(p,q) we regard the bigraded theory MGL(p,q) as just a graded theory. There is a unique ring morphism phi: MGL(0)(k) -> Z which sends the class [X](MGL) of a smooth projective k-variety X to the Euler characteristic chi(X, O-X) of the...
• Regulator constants and the parity conjecture AI翻译
  作者：Dokchitser, Tim; Dokchitser, Vladimir
  作者单位：University of Cambridge; University of Cambridge
  摘要：The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p(infinity)-Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K-infinity is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K-infinity/Q). We also give analogous results when K/Q is non-abelian, the ba...
• The quantum McKay correspondence for polyhedral singularities AI翻译
  作者：Bryan, Jim; Gholampour, Amin
  作者单位：University of British Columbia; California Institute of Technology
  摘要：Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity a,(3)/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over th...
• Rationally isotropic quadratic spaces are locally isotropic AI翻译
  作者：Panin, Ivan
  作者单位：University of Bielefeld
  摘要：Let R be a regular local ring, K its field of fractions and (V,phi) a quadratic space over R. Assume that R contains a field of characteristic zero we show that if (V,phi)aS- (R) K is isotropic over K, then (V,phi) is isotropic over R. This solves the characteristic zero case of a question raised by J.-L. Colliot-Th,lSne in [3]. The proof is based on a variant of a moving lemma from [7]. A purity theorem for quadratic spaces is proved as well. It generalizes in the charactersitic zero case the...
• The Gersten conjecture for Milnor K-theory AI翻译
  作者：Kerz, Moritz
  作者单位：University of Regensburg
  摘要：We prove that the n-th Milnor K-group of an essentially smooth local ring over an infinite field coincides with the (n,n)-motivic cohomology of the ring. This implies Levine's generalized Bloch-Kato conjecture.
• The stable free rank of symmetry of products of spheres AI翻译
  作者：Hanke, Bernhard
  作者单位：University of Munich
  摘要：A well known conjecture in the theory of transformation groups states that if p is a prime and (acurrency sign/p) (r) acts freely on a product of k spheres, then ra parts per thousand currency signk. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non-simply connected spaces.