-
作者：Dunfield, Nathan M.; Garoufalidis, Stavros; Rubinstein, J. Hyam
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Southern University of Science & Technology; University of Melbourne
摘要：We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds. Our main result is that the count of (possibly disconnected) essential surfaces in terms of their Euler characteristic always has a short generating function and hence has quasi-polynomial behavior. This gives remarkably concise formulae for the number of such surfaces, as well as detailed asymptotics. We give algori...
-
作者：Balister, Paul; Bollobas, Bela; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius
作者单位：University of Oxford; University of Memphis; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Since their introduction by Erdos in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding the existence of covering systems with various properties. In particular, Erdos asked if the moduli can be distinct and all arbitrarily large, Erdos and Selfridge asked if themoduli can be distinct and all odd, and Schinzel conjectured that in any covering syst...
-
作者：Briggs, Benjamin
作者单位：Utah System of Higher Education; University of Utah
摘要：For any ideal I of finite projective dimension in a commutative noetherian local ring R, we prove that if the conormal module I/I-2 has finite projective dimension over R/I, then I must be generated by a regular sequence. This resolves a conjecture of Vasconcelos. We prove a similar result for the first Koszul homology module of I. When R is a localisation of a polynomial ring over a field K of characteristic zero, Vasconcelos conjectured that R/I is a reduced complete intersection if the modu...
-
作者：Carmeli, Shachar; Schlank, Tomer M.; Yanovski, Lior
作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; Max Planck Society
摘要：We extend the theory of ambidexterity developed by M. J. Hopkins and J. Lurie and show that the infinity-categories of T (n)-local spectra are infinity-semiadditive for all n, where T (n) is the telescope on a vn-self map of a type n spectrum. This generalizes and provides a newproof for the analogous result of Hopkins-Lurie on K(n)-local spectra. Moreover, we showthat K(n)-local and T (n)-local spectra are respectively, the minimal and maximal 1-semiadditive localizations of spectra with resp...
-
作者：Ghosh, Amit; Sarnak, Peter
作者单位：Oklahoma State University System; Oklahoma State University - Stillwater; Institute for Advanced Study - USA; Princeton University
摘要：For integers k, we consider the affine cubic surface V-k given by M(x) = x(1)(2) + x(2)(2) + x(3)(2) - x(1)x(2)x(3) = k. We show that for almost all k the Hasse Principle holds, namely that V-k(Z) is non-empty if V-k(Z(p)) is non-empty for all primes p, and that there are infinitely many k's for which it fails. The Markoff morphisms act on V-k(Z) with finitely many orbits and a numerical study points to some basic conjectures about these class numbers and Hasse failures. Some of the analysis m...
-
作者：Angles, Bruno; Tuan Ngo Dac; Ribeiro, Floric Tavares
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Caen Normandie
摘要：In 2012 Taelman proved a class formula for Drinfeld F-q[t]-modules. For an arbitrary coefficient ring A, several deep but partial results in the direction of a class formula for Drinfeld A-modules have been obtained. In this paper, using a completely new approach based on the notion of Stark units, we establish the class formula for Drinfeld A-modules in full generality. Further we extend this class formula for A-finite or abelian Anderson modules and more generally for admissible Anderson mod...
-
作者：Stokman, J., V; Reshetikhin, N.
作者单位：University of Amsterdam; Tsinghua University; Saint Petersburg State University
摘要：Let G be a split real connected Lie group with finite center. In the first part of the paper we define and study formal elementary spherical functions. They are formal power series analogues of elementary spherical functions on G in which the role of the quasi-simple admissible G-representations is replaced by Verma modules. For generic highest weight we express the formal elementary spherical functions in terms of Harish-Chandra series and integrate them to spherical functions on the regular ...
-
作者：Carrasco, Matias; Mackay, John M.
作者单位：Universidad de la Republica, Uruguay; University of Bristol
摘要：We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without 2-torsion) have confo...
