2期

最新文章

• A transcendental Julia set of dimension 1 AI翻译
  作者：Bishop, Christopher J.
  作者单位：State University of New York (SUNY) System; Stony Brook University
  摘要：We construct a non-polynomial entire function whose Julia set has finite 1-dimensional spherical measure, and hence Hausdorff dimension 1. In 1975, Baker proved the dimension of such a Julia set must be at least 1, but whether this minimum could be attained has remained open until now. Our example also has packing dimension 1, and is the first transcendental Julia set known to have packing dimension strictly less than 2. It is also the first example with a multiply connected wandering domain w...
• Algebraic K-theory and descent for blow-ups AI翻译
  作者：Kerz, Moritz; Strunk, Florian; Tamme, Georg
  作者单位：University of Regensburg
  摘要：We prove that algebraic K-theory satisfies 'pro-descent' for abstract blow-up squares of noetherian schemes. As an application we derive Weibel's conjecture on the vanishing of negative K-groups.
• Arithmetic representations of fundamental groups I AI翻译
  作者：Litt, Daniel
  作者单位：Columbia University
  摘要：Let X be a normal algebraic variety over a finitely generated field k of characteristic zero, and let be a prime. Say that a continuous adic representation of et 1 (X k) is arithmetic if there exists a finite extension k of k, and a representation. of p et 1 (Xk ), with. a subquotient of. p1(Xk). We show that there exists an integer N = N(X) such that every nontrivial, semisimple arithmetic representation of p et 1 (X) is nontrivial mod N. As a corollary, we prove that any nontrivial - adic re...
• The Galois action on geometric lattices and the mod- I/OM AI翻译
  作者：Topaz, Adam
  作者单位：University of Oxford
  摘要：This paper studies the Galois action on a special lattice of geometric origin, which is related to mod- abelian-by-central quotients of geometric fundamental groups of varieties. As a consequence, we formulate and prove the mod- abelian-by-central variant/strengthening of a conjecture due to Ihara/Oda-Matsumoto.
• Holomorphic anomaly equations and the Igusa cusp form conjecture AI翻译
  作者：Oberdieck, Georg; Pixton, Aaron
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：Let S be a K3 surface and let E be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold for all curve classes which are primitive in the K3 factor. In particular, we deduce the Igusa cusp form conjecture. The proof relies on new results in the Gromov-Witten theory of elliptic curves and K3 surfaces. We show the generating series of Gromov-Witten classes of an elliptic curve are cycle-valued quasimodular forms and satisfy a holomorphic anomaly equation. The q...
• Counting and effective rigidity in algebra and geometry AI翻译
  作者：Linowitz, Benjamin; McReynolds, D. B.; Pollack, Paul; Thompson, Lola
  作者单位：University System of Ohio; Oberlin College; Purdue University System; Purdue University; University System of Georgia; University of Georgia
  摘要：The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manif...