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作者：Hartl, Urs
摘要：We develop the analog in equal positive characteristic of Fontaine's theory for crystalline Galois representations of a p-adic field. In particular we describe the analog of Fontaine's functor which assigns to a crystalline Galois representation an isocrystal with a Hodge filtration. In equal characteristic the role of isocrystals and Hodge filtrations is played by z-isocrystals and Hodge-Pink structures. The latter were invented by Pink. Our first main result in this article is the analog of ...
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作者：Braverman, Alexander; Kazhdan, David
摘要：We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake isomorphism for this algebra, relating it to integrable representations of the Langlands dual affine Kac-Moody group. In the next publication we shall use these results to define and study the notion of Hecke eigenfunction for the group G(aff).
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作者：Caffarell, Luis; Silvestre, Luis
摘要：We prove a regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classical sense. If we let the order of the equation approach two, we recover the theorem of Evans and Krylov about the regularity of solutions to concave uniformly elliptic partial differential equations.
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作者：Hamel, Francois; Nadirashvili, Nikolai; Russ, Emmanuel
摘要：Let Omega be a bounded C-2 domain in R-n, where n is any positive integer, and let Omega* be the Euclidean ball centered at 0 and having the same Lebesgue measure as Omega. Consider the operator L = -div(A del) v . del + V on Omega with Dirichlet boundary condition, where the symmetric matrix field A is in W-1,W-infinity(Omega), the vector field v is in L-infinity(Omega, R-n) and V is a continuous function in (Omega) over bar. We prove that minimizing the principal eigenvalue of L when the Leb...
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作者：Voevodsky, Vladimir
摘要：In this paper we prove the conjecture of Bloch and Kato which relates Milnor's K-theory of a field with its Galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the Nisnevich and etale topologies.
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作者：Guth, Larry
摘要：We prove two lower bounds for the volumes of balls in a Riemannian manifold. If (M-n, g) is a complete Riemannian manifold with filling radius at least R, then it contains a ball of radius R and volume at least delta(n)R-n If (M-n, hyp) is a closed hyperbolic manifold and if g is another metric on M with volume no greater than delta(n)Vol(M, hyp), then the universal cover of (M, g) contains a unit ball with volume greater than the volume of a unit ball in hyperbolic n-space.
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作者：Shin, Sug Woo
摘要：Our aim is to establish some new cases of the global Langlands correspondence for GL(m). A long the way we obtain a new result on the description of the cohomology of some compact Shimura varieties. Let F be a CM field with complex conjugation c and II be a cuspidal automorphic representation of GL(m)(A(F)). Suppose that II similar to II o c and that II infinity is cohomological. A very mild conditionon II infinity is imposed if m is even. We prove that for each prime l there exists a continuo...
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作者：Rottenfusser, Guenter; Rueckert, Johannes; Rempe, Lasse; Schleicher, Dierk
摘要：We construct an entire function in the Eremenko-Lyubich class B whose Julia set has only bounded path-components. This answers a question of Eremenko from 1989 in the negative. On the other hand, we show that for many functions in B, in particular those of finite order, every escaping point can be connected to infinity by a curve of escaping points. This gives a partial positive answer to the aforementioned question of Eremenko, and answers a question of Fatou from 1926.
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作者：Foreman, Matthew; Rudolph, Daniel J.; Weiss, Benjamin
摘要：All common probability preserving transformations can be represented as elements of MPT, the group of measure preserving transformations of the unit interval with Lebesgue measure. This group has a natural Polish topology and the induced topology on the set of ergodic transformations is also Polish. Our main result is that the set of ergodic elements T in MPT that are isomorphic to their inverse is a complete analytic set. This has as a consequence the fact that the isomorphism relation is als...
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作者：Bilu, Yuri; Parent, Pierre
摘要：We prove that there exists an integer p(0) such that X-split(p)(Q) is made of cusps and CM-points for any prime p > p(0). Equivalently, for any non-CM elliptic curve E over Q and any prime p > po the image of Gal((Q) over bar /Q) by the representation induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an old question of Serre.
