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作者：Li, Yingkun
作者单位：Technical University of Darmstadt
摘要：In this paper, we investigate the algebraic nature of the value of a higher Green function on an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of Gross and Zagier in the setting of higher Green functions on the product of two modular curves. In the process, we will study analogue of harmonic Maass forms in the setting of Hilbert modular forms, and obtain results concerning the arithmetic of their holomorphic part Fourier coefficients. As a consequence, we a...
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作者：Fujiwara, Koji; Sela, Zlil
作者单位：Kyoto University; Hebrew University of Jerusalem
摘要：We study the countable set of rates of growth of a hyperbolic group with respect to all its finite generating sets. We prove that the set is well-ordered, and that every real number can be the rate of growth of at most finitely many generating sets up to automorphism of the group. We prove that the ordinal of the set of rates of growth is at least omega(omega 0)(0), and in case the group is a limit group (e.g. free and surface groups) it is omega(omega 0)(0). We further study the rates of grow...
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作者：Novack, Matthew; Vicol, Vlad
作者单位：Purdue University System; Purdue University; New York University
摘要：For any regularity exponent beta < 1/2, we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class C-t(0)(H-beta & cap; L1/(1-2 beta)). By interpolation, such solutions belong to (CtB3,infinity S)-B-0 for s approaching 1/3 as beta approaches 1/2. Hence this result provides a new proof of the flexible side of the L3-based Onsager conjecture. Of equal importance is that the intermittent nature of our solutions matches that of turbulent flows, which are obs...
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作者：Gan, Wee Teck; Savin, Gordan
作者单位：National University of Singapore; Utah System of Higher Education; University of Utah
摘要：We study three exceptional theta correspondences for p-adic groups, where one member of the dual pair is the exceptional group G(2). We prove the Howe duality conjecture for these dual pairs and a dichotomy theorem, and determine explicitly the theta lifts of all non-cuspidal representations.
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作者：Bresciani, Giulio
摘要：Let X be a curve over a field k finitely generated over Q and t an indeterminate. We prove that, if s is a section of pi(1)(X) -> Gal(k) such that the base change s(k(t)) is birationally liftable, then s comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.
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作者：Bader, Uri; Fisher, David; Miller, Nicholas; Stover, Matthew
作者单位：Weizmann Institute of Science; Rice University; University of Oklahoma System; University of Oklahoma - Norman; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：For n >= 2, we prove that a finite volume complex hyperbolic n-manifold containing infinitely many maximal properly immersed totally geodesic submanifolds of real dimension at least two is arithmetic, paralleling our previous work for real hyperbolic manifolds. As in the real hyperbolic case, our primary result is a superrigidity theorem for certain representations of complex hyperbolic lattices. The proof requires developing new general tools not needed in the real hyperbolic case. Our main r...
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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...
