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作者：Blumenthal, Alex; Xue, Jinxin; Young, Lai-Sang
摘要：We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A prime example is the standard map. Lower bounds for Lyapunov exponents of such systems are very hard to estimate, due to the potential switching of stable and unstable directions. This paper shows that with the addition of (very) small random perturbations, one obtains with relative ease Lyapunov exponents reflectin...
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作者：Walker, Mark E.
摘要：The Buchsbaum-Eisenbud-Horrocks Conjecture predicts that the ith Betti number beta(i)(M) of a nonzero module M of finite length and finite projective dimension over a local ring R of dimension d should be at least ((d)(i)). It would follow from the validity of this conjecture that Sigma(i)beta(i)(M)>= 2d. We prove the latter inequality holds in a large number of cases and that, when R is a complete intersection in which 2 is invertible, equality holds if and only if M is isomorphic to the quot...
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作者：Caraiani, Ana; Scholze, Peter
摘要：The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity assumption. Along the way, we establish various foundational results on the geometry of the Hodge-Tate period map. In particular, we compare the fibres of the Hodge-Tate period map with Igusa varieties.
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作者：Ettinger, Boris; Lindblad, Hans
摘要：We are concerned with how regular initial data have to be to ensure local existence for Einstein's equations in wave coordinates. Klainerman-Rodnianski and Smith-Tataru showed that there in general is local existence for data in Sobolev spaces H<^>s with regularity s>2. We give an example of data in Sobolev spaces with regularity s=2 for which there is no local solution in this space.
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作者：Cadoret, Anna; Hui, Chun-Yin; Tamagawa, Akio
摘要：Let X be a connected scheme, smooth and separated over an algebraically closed field k of characteristic p >= 0, let f : Y -> X be a smooth proper morphism and x a geometric point on X. We prove that the tensor invariants of bounded length <= d of pi(1)(X, x) acting on the etale cohomology groups H* (Y-x, F-l) are the reduction modulo-l of those of pi(1)(X, x) acting on H* (Y-x, Z(l)) for l greater than a constant depending only on f : Y -> X, d. We apply this result to show that the geometric...
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作者：Zhang, Weiping
摘要：We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds to the case of foliated spin manifolds. As a consequence, we show that there is no foliation of positive leafwise scalar curvature on any torus, which generalizes the famous theorem of Schoen-Yau and Gromov-Lawson on the nonexistence of metrics of positive scalar curvature on torus to the case of foliations. Moreover, our method, which is partly...
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作者：Bushnell, Colin J.; Henniart, Guy
摘要：Let F be a non-Archimedean locally compact field. We show that the local Langlands correspondence over F has a strong property generalizing the higher ramification theorem of local class field theory. If pi is an irreducible cuspidal representation of a general linear group GL(n)(F) and sigma the corresponding irreducible representation of the Weil group W-F of F, the restriction of sigma to a ramification subgroup of W-F is determined by a truncation of the simple character theta(pi) containe...
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作者：Fasel, Jean
摘要：We explain a mistake that occurred in the proof of Murthys conjecture by the author.
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作者：Galatius, Soren; Randal-Williams, Oscar D.
摘要：We prove a homological stability theorem for moduli spaces of manifolds of dimension 2n, for attaching handles of index at least n, after these manifolds have been stabilised by countably many copies of S-n x S-n. Combined with previous work of the authors, we obtain an analogue of the Madsen Weiss theorem for any simply -connected manifold of dimension 2n >= 6.
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作者：Croot, Ernie; Lev, Vsevolod F.; Pach, Peter Pal
