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作者：Pop, Florian
摘要：We show that the conjecture of Oort on lifting covers of curves is true. The main ingredients in the proof are a deformation argument in charact eristic p and (a special case of) a very recent result by Obus-Wewers. A kind of boundedness result is given as well.
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作者：He, Xuhua
摘要：This paper studies affine Deligne-Lusztig varieties Ka, (b) in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of K(sic) (b) for a minimal length element 71; in the conjugacy class of an extended affine Weyl group. We then provide a reduction method that relates the structure of X,(sic) (b) for arbitrary elements 71; in the extended affine Weyl group to those associated with minimal length elements. Based on this reduction, we establish a con...
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作者：Bufetov, Alexander I.
摘要：The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).
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作者：Klingler, Bruno; Yafaev, Andrei
摘要：In this paper we prove, assuming the Generalized Riemann Hypothesis, the Andre-Oort conjecture on the Zariski closure of sets of special points in a Shimura variety. In the case of sets of special points satisfying an additional assumption, we prove the conjecture without assuming the GRH.
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作者：Chen, Qile
摘要：We introduce a new compactification of the space of relative stable maps. This approach uses logarithmic geometry in the sense of Kato-Fontaine-Illusie without taking expansions of the target. The underlying structures of the stable logarithmic maps are stable in the usual sense.
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作者：Kiselev, Alexander; Sverak, Vladimir
摘要：We construct an initial data for the two-dimensional Euler equation in a disk for which the gradient of vorticity exhibits double exponential growth in time for all times. This estimate is known to be sharp - the double exponential growth is the fastest possible growth rate.
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作者：Bernard, Yann; Riviere, Tristan
摘要：We prove a bubble-neck decomposition together with an energy quantization result for sequences of Willmore surfaces into R-m with uniformly bounded energy and nondegenerating conformal type. We deduce the strong compactnes of Willmore closed surfaces of a given genus modulo the Mobius group action, below some energy threshold.
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作者：Obus, Andrew; Wewers, Stefan
摘要：The local Oort conjecture states that, if Gamma is cyclic and k is an algebraically closed field of characteristic p, then all Gamma-extensions of k[[t]] should lift to characteristic zero. We prove a critical case of this conjecture. In particular, we show that the conjecture is always true when v(p) (vertical bar Gamma vertical bar) <= 3 and is true for arbitrarily highly p-divisible cyclic groups Gamma when a certain condition on higher ramification filtration is satisfied.
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作者：Pila, Jonathan; Tsimerman, Jacob
摘要：We prove the Ax-Lindemann theorem for the coarse moduli space A(g) of principally polarized abelian varieties of dimension g >= 1. We affirm the Andre-Oort conjecture unconditionally for A(g) for g <= 6, and under GRH for all g.
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作者：Nonnenmacher, Stephane; Sjoestrand, Johannes; Zworski, Maciej
摘要：We study a semiclassical quantization of Poincare maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result includes the case of several convex (hard) obstacles satisfying a no-eclipse condition.
