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作者：Grodal, J
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作者：Hoffman, C; Rudolph, D
摘要：A uniformly p-to-one endomorphism is a measure-preserving map with entropy log p which is almost everywhere p-to-one and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is a one-sided p-shift, with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite-to-one endomorphisms conjugate to this standard example by a condition on the past tree of names which is analogous to very weakly Bernoulli or loosely Bernoul...
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作者：Martel, Y; Merle, F
摘要：The generalized Korteweg-de Vries equations are a class of Hamiltonian systems in infinite dimension derived from the KdV equation where the quadratic term is replaced by a higher order power term. These equations have two conservation laws in the energy space H-1 (L-2 norm and energy). We consider in this paper the critical generalized KdV equation, which corresponds to the smallest power of the nonlinearity such that the two conservation laws do not imply a bound in H-1 uniform in time for a...
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作者：DeBacker, S
摘要：Let k denote a field with nontrivial discrete valuation. We assume that k is complete with perfect residue field. Let G be the group of k-rational points of a reductive, linear algebraic group defined over k. Let g denote the Lie algebra of G. Fix r is an element of R. Subject to some restrictions, we show that the set of distinguished degenerate Moy-Prasad cosets of depth r (up to an equivalence relation) parametrizes the nilpotent orbits in g.
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作者：Ulmer, D
摘要：We produce explicit elliptic curves over F-p(t) whose Mordell-Weil groups have arbitrarily large rank. Our method is to prove the conjecture of Birch and Swinnerton-Dyer for these curves (or rather the Tate conjecture for related elliptic surfaces) and then use zeta functions to determine the rank. In contrast to earlier examples of Shafarevitch and Tate, our curves are not isotrivial. Asymptotically these curves have maximal rank for their conductor. Motivated by this fact, we make a conjectu...
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作者：Hughes, B
摘要：Skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations (under dimension and compactness assumptions). In general, the stratified approximate fibrations cannot be replaced by bundles, and the teardrops cannot be replaced by mapping cylinder neighborhoods. Thus, this is the best possible topological tubular neighborhood theorem in the stratified setting.
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作者：Badzioch, B
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作者：Long, YM; Zhu, CF
摘要：For any given compact C-2 hypersurface Sigma in R-2n bounding a strictly convex set with nonempty interior, in this paper an invariant p(n)(Sigma) is defined and satisfies p(n)(Sigma) greater than or equal to [n/2] + 1, where [a] denotes the greatest integer which is not greater than a c R. The following results are proved in this paper. There always exist at least p(n)(Sigma) geometrically distinct closed characteristics on E. If all the geometrically distinct closed characteristics on E are ...
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作者：Auscher, P; Hofmann, S; Lacey, M; McIntosh, A; Tchamitchian, P
摘要：We prove the Kato conjecture for elliptic operators on R-n. More precisely, we establish that the domain of the square root of a uniformly complex elliptic operator L = -div (Adel) with bounded measurable coefficients in R-n is the Sobolev space H-1(R-n) in any dimension with the estimate parallel torootLfparallel to(2) similar to parallel todelfparallel to(2).
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作者：Milne, JS
摘要：We prove that Grothendieck's Hodge standard conjecture holds for abelian varieties in arbitrary characteristic if the Hodge conjecture holds for complex abelian varieties of CM-type. For abelian varieties with no exotic algebraic classes, we prove the Hodge standard conjecture unconditionally.
