Annals of Mathematics

最新文章

• Quantization of coboundary Lie bialgebras AI翻译
  作者：Enriquez, Benjamin; Halbout, Gilles
  摘要：We show that any coboundary Lie bialgebra can be quantized. For this, we prove that Etingof-Kazhdan quantization functors are compatible with Lie bialgebra twists, and if such a quantization functor corresponds to an even associator, then it is also compatible with the operation of taking coopposites. We also use the relation between the Etingof-Kazhdan construction of quantization functors and the alternative approach to this problem, which was established in a previous work. Let k be a field...
• The density of discriminants of quintic rings and fields AI翻译
  作者：Bhargava, Manjul
• The spectral edge of some random band matrices AI翻译
  作者：Sodin, Sasha
  摘要：We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the band is sufficiently wide (W >> N-5/6). Otherwise, a different limiting distribution appears.
• Canonical subgroups of Barsotti-Tate groups AI翻译
  作者：Tian, Yichao
  摘要：Let S be the spectrum of a complete discrete valuation ring with fraction field of characteristic 0 and perfect residue field of characteristic p >= 3. Let G be a truncated Barsotti-Tate group of level 1 over S. If G is not too supersingular, a condition that will be explicitly expressed in terms of the valuation of a certain determinant, then we prove that we can canonically lift the kernel of the Frobenius endomorphism of its special fiber to a subgroup scheme of G, finite and flat over S. W...
• Perturbations of orthogonal polynomials with periodic recursion coefficients AI翻译
  作者：Damanik, David; Killip, Rowan; Simon, Barry
  摘要：The results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon are extended from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations.
• Measure equivalence rigidity of the mapping class group AI翻译
  作者：Kida, Yoshikata
  摘要：We show that the mapping class group of a compact orientable surface with higher complexity satisfies the following rigidity in the sense of measure equivalence: If the mapping class group is measure equivalent to a discrete group, then they are commensurable up to finite kernels. Moreover, we describe all locally compact second countable groups containing a lattice isomorphic to the mapping class group. We obtain similar results for finite direct products of mapping class groups.
• On the classification of finite-dimensional pointed Hopf algebras AI翻译
  作者：Andruskiewitsch, Nicolas; Schneider, Hans-Juergen
  摘要：We classify finite-dimensional complex Hopf algebras A which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements G(A) is abelian such that all prime divisors of the order of G (A) are > 7. Since these Hopf algebras turn out to be deformations of a natural class of generalized small quantum groups, our result can be read as an axiomatic description of generalized small quantum groups.
• On the formation of singularities in the critical O(3) σ-model AI翻译
  作者：Rodnianski, Igor; Sterbenz, Jacob
  摘要：We study the phenomena of energy concentration for the critical O(3) sigma model, also known as the wave map flow from R2+1 Minkowski space into the sphere S-2. We establish rigorously and constructively existence of a set of smooth initial data resulting in a dynamic finite time formation of singularities. The construction and analysis are done in the context of the k-equivariant symmetry reduction, and we restrict to maps with homotopy class k >= 4. The concentration mechanism we uncover is ...
• A nonhomogeneous orbit closure of a diagonal subgroup AI翻译
  作者：Maucourant, Francois
  摘要：Let G = SLl(n, R) with n >= 6. We construct examples of lattices F C G, subgroups A of the diagonal group D and points x is an element of G/Gamma such that the closure of the orbit Ax is not homogeneous and such that the action of A does not factor through the action of a one-parameter nonunipotent group. This contradicts a conjecture of Margulis.
• Local rigidity of partially hyperbolic actions I. KAM method and Zk actions on the torus AI翻译
  作者：Damjanovic, Danijela; Katok, Anatole
  摘要：We show C-infinity local rigidity for Z(k) (k >= 2) higher rank partially hyperbolic actions by toral automorphisms, using a generalization of the KAM (Kolmogorov-Arnold- Moser) iterative scheme. We also prove the existence of irreducible genuinely partially hyperbolic higher rank actions on any torus T-N for any even N >= 6.