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作者：Roendigs, Oliver
作者单位：University Osnabruck
摘要：The endomorphism ring of the projective plane over a field F of characteristic neither two nor three is slightly more complicated in the Morel-Voevodsky motivic stable homotopy category than in Voevodsky's derived category of motives. In particular, it is not commutative precisely if there exists a square in F which does not admit a sixth root. A byproduct of these computations is a proof of Suslin's conjecture on the Suslin-Hurewicz homomorphism from Quillen to Milnor K-theory in degree four,...
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作者：Avila, Artur; Damanik, David; Zhang, Zhenghe
作者单位：University of Zurich; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Rice University; University of California System; University of California Riverside
摘要：We consider discrete one-dimensional Schrodinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant Holder continuous function defined on a subshift of finite type with a fully supported ergodic measure admitting a local product structure and a fixed point, then the Lyapunov exponent is positive away from a discrete set of energies. Moreover, for sampling functions i...
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作者：Ma, Linquan
作者单位：Purdue University System; Purdue University
摘要：The long standing Lech's conjecture in commutative algebra states that for a flat local extension (R, m) -> (S, n) of Noetherian local rings, we have an inequality on the Hilbert-Samuel multiplicities: e(R) <= e(S). In general the conjecture is wide open when dim R > 3, even in equal characteristic. In this paper, we prove Lech's conjecture in all dimensions, provided (R, m) is a standard graded ring over a perfect field localized at the homogeneous maximal ideal. We introduce the notions of l...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The main focus of this article concerns the strongly percolative regime of the vacant set of random interlacements on Z(d), d = 3. We investigate the occurrence in a large box of an excessive fraction of sites that get disconnected by the interlacements from the boundary of a concentric box of double size. The results significantly improve our findings in Sznitman (Probab. Math. Phys. 2-3:563-311, 2021). In particular, if, as expected, the critical levels for percolation and for strong percola...
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作者：Nelson, Paul D.
作者单位：Aarhus University
摘要：Let (pi, sigma) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan-Gross-Prasad pair (Un+1, U-n) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local con-ditions (in particular, temperedness). We prove that the subconvex bound L(pi x sigma, 1/2) << C(pi x sigma )(1/4-delta...
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作者：Belov, Yurii; Kulikov, Aleksei; Lyubarskii, Yurii
作者单位：Norwegian University of Science & Technology (NTNU)
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作者：Italiano, Giovanni; Martelli, Bruno; Migliorini, Matteo
作者单位：Scuola Normale Superiore di Pisa
摘要：We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence, we build a finite type subgroup of a hyperbolic group that is not hyperbolic.
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作者：Alper, Jarod; Halpern-Leistner, Daniel; Heinloth, Jochen
作者单位：University of Washington; University of Washington Seattle; Cornell University; University of Duisburg Essen
摘要：We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a T-stratification. These results provide a generalization of the Keel-Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to constr...
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作者：Ivanov, Sergei; Mamaev, Daniil; Nordskova, Anya
作者单位：Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; Hasselt University
摘要：We prove that if all intersections of a convex body B subset of R-4 with 3-dimensional linear subspaces are linearly equivalent then B is a centered ellipsoid. This gives an affirmative answer to the case n = 3 of the following question by Banach from 1932: Is a normed vector space V whose n-dimensional linear subspaces are all isometric, for a fixed 2 <= n < dim V, necessarily Euclidean? The dimensions n = 3 and dim V = 4 is the first case where the question was unresolved. Since the 3-sphere...
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作者：Lindenstrauss, E.; Mohammadi, A.
作者单位：Hebrew University of Jerusalem; University of California System; University of California San Diego
摘要：We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL2(R) in arithmetic quotients of SL2(C) and SL2(R) x SL2(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.
