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• Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation AI翻译
  作者：Kings, Guido; Sprang, Johannes
  摘要：We show that for an arbitrary totally complex number field L the (regularized) critical L-values of algebraic Hecke characters of L divided by certain periods are algebraic integers. This relies on a new construction of an equivariant coherent cohomology class with values in the completion of the Poincare bundle on an abelian scheme A. From this we obtain a cohomology class for the automorphism group of a CM abelian scheme A with values in some canonical bundles, which can be explicitly calcul...
• Fundamental groups and the Milnor conjecture AI翻译
  作者：Brue, Elia; Naber, Aaron; Semola, Daniele
  摘要：It was conjectured by Milnor in 1968 that the fundamental group of a complete manifold with nonnegative Ricci curvature is finitely generated. The main result of this paper is a counterexample, which provides an example M-7 with Ric >= 0 such that pi 1(M) = Q/Z is infinitely generated. There are several new points behind the result. The first is a new topological construction for building manifolds with infinitely generated fundamental groups, which can be interpreted as a smooth version of th...
• Galois sections and p-adic period mappings AI翻译
  作者：Betts, L. alexander; Stix, Jakob
  摘要：Let K be a number field not containing a CM subfield. For any smooth projective curve Y/K of genus >= 2, we prove that the image of the Selmer part of Grothendieck's section set inside the Kv-rational points Y (Kv) is finite for every finite place v. This gives an unconditional verification of a prediction of Grothendieck's section conjecture. In the process of proving our main result, we also refine and extend the method of Lawrence and Venkatesh, with potential consequences for explicit comp...
• Weil-Petersson curves, β-numbers, and minimal surfaces AI翻译
  作者：Bishop, Christopher J.
  摘要：This paper gives geometric characterizations of the Weil-Petersson class of rectifiable quasicircles, i.e., the closure of the smooth planar curves in the Weil-Petersson metric on universal Teichmuller space defined by Takhtajan and Teo. Although motivated by the planar case, many of our characterizations make sense for curves in Rn and remain equivalent in all dimensions. We prove that Gamma is Weil-Petersson if and only if it is well approximated by polygons in a precise sense, has finite Mo...
• Complete classification of global solutions to the obstacle problem AI翻译
  作者：Eberle, Simon; Figalli, Alessio; Weiss, Georg s.
  摘要：The characterization of global solutions to the obstacle problems in RN, or equivalently of null quadrature domains, has been studied for more than 90 years. In this paper, we give a conclusive answer to this problem by proving the following long-standing conjecture: The coincidence set of a global solution to the obstacle problem is either a half-space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.
• Fractal uncertainty in higher dimensions AI翻译
  作者：Cohen, Alex
  摘要：We prove that if a fractal set in Rd avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main ingredient is a new higher-dimensional Beurling-Malliavin multiplier theorem.
• On approximation to a real number by algebraic numbers of bounded degree AI翻译
  作者：Poels, Anthony
  摘要：In his seminal 1961 paper, Wirsing studied how well a given transcendental real number xi can be approximated by algebraic numbers alpha of degree at most n for a given positive integer n , in terms of the so-called naive height H(alpha) of alpha . He showed that the supremum omega & lowast;n(xi) of all omega for which infinitely many such alpha have |xi- alpha| <= H(alpha)-omega-1 is at least (n + 1)/2. He also asked if we could even have omega & lowast;n(xi) >= nas it is generally expected. ...
• Topological central extensions of semi-simple groups over local fields by Gopal Prasad and M. S. Raghunathan (vol 119, pg 143, 1984) AI翻译
  作者：Prasad, Gopal
• Grid diagrams and Heegaard Floer invariants AI翻译
  作者：Manolescu, Ciprian; Ozsvath, Peter s.; Thurston, Dylan p.
  摘要：We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2Z). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descriptions of the mod 2 Ozsv & aacute;th-Szab & oacute; mixed invariants of closed four-manifolds, also in terms of grid diagrams.
• Effective version of Ratner's equidistribution theorem for SL(3, R) AI翻译
  作者：Yang, Lei
  摘要：In this paper, we will prove an effective version of Ratner's equidistribution theorem for unipotent orbits in SL(3, R)/SL(3, Z) with a natural Diophantine condition.