Annals of Mathematics

最新文章

• Curves and symmetric spaces, II AI翻译
  作者：Mukai, Shigeru
  摘要：Let Sym(3) C -> P-*(k circle plus Sym(3) k circle plus Sym(3) k circle plus k) = P-13, A bar right arrow (1 : A : A' : det A) be the Veronese embedding of the space of symmetric matrices of degree 3, where A' is the cofactor matrix of A. The closure SpG(3, 6) of this image is a 6-dimensional homogeneous variety of the symplectic group Sp(3). A canonical curve C-16 subset of P-8 of genus 9 over a perfect field k is isomorphic to a complete linear section of this projective variety SpG(3, 6) sub...
• A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver AI翻译
  作者：Aschbacher, Michael; Chermak, Andrew
  摘要：We extend the notion of a p-local finite group (defined in [BLO03]) to the notion of a p-local group. We define morphisms of p-local groups, obtaining thereby a category, and we introduce the notion of a representation of a p-local group via signalizer functors associated with groups. We construct a chain & = (g(0) -> g(1) -> ... ) of 2-local finite groups, via a representation of a chain &* = (G(0) G(1) -> ... ) of groups, such that g(0) is the 2-local finite group of the third Conway sporadi...
• Arithmetic quantum unique ergodicity for symplectic linear maps of the multidimensional torus AI翻译
  作者：Kelmer, Dubi
  摘要：We look at the expectation values for quantized linear symplectic maps on the multidimensional torus and their distribution in the semiclassical limit. We construct super-scars that are stable under the arithmetic symmetries of the system and localize on invariant manifolds. We show that these super-scars exist only when there are isotropic rational subspaces, invariant under the linear map. In the case where there are no such scars, we compute the variance of the fluctuations of the matrix el...
• The Iwasawa μ-invariant of p-adic Hecke L-functions AI翻译
  作者：Hida, Haruzo
  摘要：For an odd prime p, we compute the mu-invariant of the anticyclotomic Katz p-adic L-function of a p-ordinary CM field if the conductor of the branch character is a product of primes split over the maximal real subfield. Except for rare cases where the root number of the p-adic functional equation is congruent to - 1 modulo p, the invariant vanishes.
• Quantum unique ergodicity for SL2(Z)\H AI翻译
  作者：Soundararajan, Kannan
  摘要：We eliminate the possibility of escape of mass for Hecke-Maass forms of large eigenvalue for the modular group. Combined with the work of Lindenstrauss, this establishes the Quantum Unique Ergodicity conjecture of Rudnick and Sarnak for Hecke-Maass forms on the modular surface SL2(Z)\H.
• Characterizing Jacobians via trisecants of the Kummer variety AI翻译
  作者：Krichever, Igor
  摘要：We prove Welters' trisecant conjecture: an indecomposable principally polarized abelian variety X is the Jacobian of a curve if and only if there exists a trisecant of its Kummer variety K(X).
• Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups AI翻译
  作者：Vaserstein, Leonid
  摘要：A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.
• The classification of Kleinian surface groups, I: models and bounds AI翻译
  作者：Minsky, Yair
  摘要：We give the first part of a proof of Thurston's Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a Lipschitz model for the thick part of the corresponding hyperbolic manifold. This enables us to describe the topological structure of the thick part, and to give a priori geometric bounds.
• Flops, motives, and invariance of quantum rings AI翻译
  作者：Lee, Yuan-Pin; Lin, Hui-Wen; Wang, Chin-Lung
  摘要：For ordinary flops, the correspondence defined by the graph closure is shown to give equivalence of Chow motives and to preserve the Poincare pairing. In the case of simple ordinary flops, this correspondence preserves the big quantum cohomology ring after an analytic continuation over the extended Kahler moduli space. For Mukai flops, it is shown that the birational map for the local models is deformation equivalent to isomorphisms. This implies that the birational map induces isomorphisms on...
• On a class of II1 factors with at most one Cartan subalgebra AI翻译
  作者：Ozawa, Narutaka; Popa, Sorin
  摘要：We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(F-r) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q (circle times) over barL(F-r), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure-preserving action of a free group F-r, 2 <= r <= infinity, on a probability space (X, mu) is profinite then the group measure space factor L-in...