Annals of Mathematics

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• The quantization conjecture revisited AI翻译
  作者：Teleman, C
  摘要：A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X, L), the cohomologies of L over the GIT quotient X parallel toG equal the invariant part of the cohomologies over X. This generalizes the theorem of CGS] on global sections, and strengthens its subsequent extensions ([JK], [MI) to Riemann-Roch numbers. Remarkable by-products are the invariance of cohomology of vector bundles over X//G und...
• Rational connectedness and Galois covers of the projective line AI翻译
  作者：Colliot-Thélène, JL
• The symplectic Thom conjecture AI翻译
  作者：Ozsváth, P; Szabó, Z
  摘要：In this paper, we demonstrate a relation among Seiberg-Witten invariants which arises from embedded surfaces in four-manifolds whose self-intersection number is negative. These relations, together with Taubes' basic theorems on the Seiberg-Witten invariants of symplectic manifolds, are then used to prove the symplectic Them conjecture: a symplectic surface in a symplectic four-manifold is genus-minimizing in its homology class. Another corollary of the relations is a general adjunction inequal...
• An improved bound on the Minkowski dimension of Besicovitch sets in R3 AI翻译
  作者：Katz, NH; Laba, I; Tao, T
  摘要：A Besicovitch set is a set which contains a unit line segment in any direction. It is known that the Minkowski and Hausdorff dimensions of such a set must be greater than or equal to 5/2 in R-3. In this paper we show that the Minkowski dimension must in fact be greater than 5/2 + epsilon for some absolute constant epsilon > 0. One observation arising from the argument is that Besicovitch sets of near-minimal dimension have to satisfy certain strong properties, which we call stickiness, planine...
• On p-divisible groups, finite groups and filtered modules AI翻译
  作者：Luce, A; Breuil, P
• Regularity of a free boundary with application to the Pompeiu problem AI翻译
  作者：Caffarelli, LA; Karp, L; Shahgholian, H
  摘要：In the unit ball B(0, 1), let u and Omega (a domain in R-N) salve the following overdetermined problem: Delta u = chi(Omega) in B(0, 1), 0 is an element of partial derivative Omega, u = \del u\ = 0 in B(0, 1) \ Omega, where chi(Omega) denotes the characteristic function, and the equation is satisfied in the sense of distributions. If the complement of Omega does not develop cusp singularities at the origin then we prove partial derivative Omega is analytic in some small neighborhood of the ori...
• Modularity of the Rankin-Selberg L-series, and multiplicity one for SL(2) (vol 152, pg 45, 2000) AI翻译
  作者：Ramakrishnan, D
• Nonvanishing of quadratic dirichlet L-functions at s=1/2 AI翻译
  作者：Soundararajan, K
• The Tits alternative for out(Fn) I: Dynamics of exponentially-growing automorphisms AI翻译
  作者：Bestvina, M; Feighn, M; Handel, M
• Construction of boundary invariants and the logarithmic singularity of the Bergman kernel AI翻译
  作者：Hirachi, K