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• Algebraic cobordism revisited AI翻译
  作者：Levine, M.; Pandharipande, R.
  作者单位：Northeastern University; Princeton University
  摘要：We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined by Levine and Morel. Double point cobordism provides a simple, geometric presentation of algebraic cobordism theory. As a corollary, the Lazard ring given by products of projective spaces rationally generates all nonsingular projective varieties modulo doubl...
• Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces AI翻译
  作者：Einsiedler, M.; Margulis, G.; Venkatesh, A.
  作者单位：University System of Ohio; Ohio State University; Yale University; Stanford University
  摘要：We prove effective equidistribution, with polynomial rate, for large closed orbits of semisimple groups on homogeneous spaces, under certain technical restrictions (notably, the acting group should have finite centralizer in the ambient group). The proofs make extensive use of spectral gaps, and also of a closing lemma for such actions.
• Knot Floer homology detects fibred knots (vol 170, pg 577, 2007) AI翻译
  作者：Ni, Yi
  作者单位：Massachusetts Institute of Technology (MIT)
• Simplicity and superrigidity of twin building lattices AI翻译
  作者：Caprace, Pierre-Emmanuel; Remy, Bertrand
  作者单位：Universite Catholique Louvain; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non-positively curved twinned buildings: those are the most important (but not the only) examples of twin building lattices. We prove that these lattices are simple if the corresponding buildings are irreducible and not of affine type (i.e. they are not Bruhat-Tits buildings). Many of them are finitely presented and enj...
• Limiting Carleman weights and anisotropic inverse problems AI翻译
  作者：Ferreira, David Dos Santos; Kenig, Carlos E.; Salo, Mikko; Uhlmann, Gunther
  作者单位：Universite Paris 13; University of Chicago; University of Helsinki; University of Washington; University of Washington Seattle
  摘要：In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig et al. (Ann. Math. 165: 567-591, 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic ray tr...
• 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.
• 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 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 period map for cubic fourfolds AI翻译
  作者：Looijenga, Eduard
  作者单位：Utrecht University
  摘要：The period map for cubic fourfolds takes values in a locally symmetric variety of orthogonal type of dimension 20. We determine the image of this period map (thus confirming a conjecture of Hassett) and give at the same time a new proof of the theorem of Voisin that asserts that this period map is an open embedding. An algebraic version of our main result is an identification of the algebra of SL (6,a,)-invariant polynomials on the representation space Sym (3)(a,(6))(*) with a certain algebra ...
• Menger's theorem for infinite graphs AI翻译
  作者：Aharoni, Ron; Berger, Eli
  作者单位：Technion Israel Institute of Technology; University of Haifa
  摘要：We prove that Menger's theorem is valid for infinite graphs, in the following strong version: let A and B be two sets of vertices in a possibly infinite digraph. Then there exist a set P of disjoint A-B paths, and a set S of vertices separating A from B, such that S consists of a choice of precisely one vertex from each path in P. This settles an old conjecture of Erdos.