2025

最新文章

• Galois sections and p-adic period mappings AI翻译
  作者：Betts, L. alexander; Stix, Jakob
  作者单位：Cornell University; Goethe University Frankfurt
  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...
• 撤稿声明: The stable Adams conjecture and higher associative structures on Moore spectra AI翻译
  作者：Bhattacharya, Prasit; Kitchloo, Nitu
  作者单位：New Mexico State University; Johns Hopkins University
• Hessian estimates for the sigma-2 equation in dimension four AI翻译
  作者：Shankar, Ravi; Yuan, Yu
  作者单位：Princeton University; University of Washington; University of Washington Seattle
  摘要：We derive a priori interior Hessian estimates and interior regularity for the sigma 2 equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher (n >= 5) dimensions.
• Weil-Petersson curves, β-numbers, and minimal surfaces AI翻译
  作者：Bishop, Christopher J.
  作者单位：State University of New York (SUNY) System; Stony Brook University
  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...
• On a conjecture of Marton AI翻译
  作者：Gowers, W. T.; Green, Ben; Manners, Freddie; Tao, Terence
  作者单位：Universite PSL; College de France; University of Cambridge; University of Oxford; University of California System; University of California San Diego; University of California System; University of California Los Angeles
  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.
• De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean AI翻译
  作者：Heikkila, Susanna; Pankka, Pekka
  作者单位：University of Jyvaskyla; University of Helsinki
  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.
• Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation AI翻译
  作者：Kings, Guido; Sprang, Johannes
  作者单位：University of Regensburg; University of Duisburg Essen
  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...
• Mod-p Poincare Duality in p-adic analytic geometry AI翻译
  作者：Zavyalov, Bogdan
  作者单位：Princeton University; Institute for Advanced Study - USA
  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,...
• 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
  作者单位：University of Michigan System; University of Michigan
• Fundamental groups and the Milnor conjecture AI翻译
  作者：Brue, Elia; Naber, Aaron; Semola, Daniele
  作者单位：Bocconi University; Northwestern University; Institute for Advanced Study - USA; Princeton University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Vienna
  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...