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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...
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作者：Gowers, W. T.; Green, Ben; Manners, Freddie; Tao, Terence
摘要：We prove a conjecture of K. Marton, widely known as the polynomial Freiman-Ruzsa conjecture, in characteristic 2. The argument extends to odd characteristic, with details to follow in a subsequent paper.
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作者：Heikkila, Susanna; Pankka, Pekka
摘要：We show that, if a closed, connected, and oriented Riemannian n-manifold N admits a non-constant quasiregular mapping from the Euclidean nspace Rn, then the de Rham cohomology algebra H & lowast;dR(N) of N embeds into the exterior algebra n & lowast;Rn. As a consequence, we obtain a homeomorphic classification of closed simply connected quasiregularly elliptic 4-manifolds.
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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...
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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...
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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...
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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.
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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.
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作者：Leslie, Spencer
摘要：We prove the endoscopic fundamental lemma for the Lie algebra of the symmetric variety U(2n)/U(n) x U(n), where U(n) denotes a unitary group of rank n. This is the first major step in the stabilization of the relative trace formula associated to the U(n) x U(n)-periods of automorphic forms on U(2n).
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作者：Zavyalov, Bogdan
摘要：We show Poincare Duality for Fp-etale cohomology of a smooth proper rigid-analytic space over a non-archimedean field K of mixed characteristic (0, p). It positively answers the question raised by P. Scholze in his paper p-adic Hodge theory for rigid-analytic varieties. We prove duality via constructing Faltings' trace map relating Poincare Duality on the generic fiber to (almost) Grothendieck Duality on the mod-p fiber of a formal model. We also formally deduce Poincare Duality for Z/pnZ, Zp,...
