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作者：D'Addezio, Marco
摘要：In this article we prove Crew's parabolicity conjecture of F-iso crystals. For this purpose, we introduce and study the notion of & DAG;-hull of a sub-F-iso-crystal. On the way, we prove a new Lefschetz theorem for overconvergent F-iso crystals.
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作者：Yu, Hongjie
摘要：Let X1 be a projective, smooth and geometrically connected curve over Fq with q = p' elements where p is a prime number, and let X be its base change to an algebraic closure of Fq. We give a formula for the number of irreducible B-adic local systems (B =6 p) with a fixed rank over X fixed by the Frobenius endomorphism. We prove that this number behaves like a Lefschetz fixed point formula for a variety over Fq, which generalises a result of Drinfeld in rank 2 and proves a conjecture of Deligne...
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作者：Fish, Joel W.; Hofer, Helmut
摘要：We prove that for each Hamiltonian function H is an element of C infinity(R4, R) defined on the standard symplectic (R4, omega 0), for which M := H-1(0) is a non-empty compact regular energy level, the Hamiltonian flow on M is not minimal. That is, we prove there exists a closed invariant subset of the Hamiltonian flow in M that is neither null nor all of M. This answers the four-dimensional case of a more than twenty year old question of Michel Herman, part of which can be regarded as a speci...
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作者：Apisa, Paul; Wright, Alex
摘要：We classify GL(2, R) orbit closures of translation surfaces of rank at least half the genus plus 1.
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作者：Kang, Dong Yeap; Kelly, Tom; Kuhn, Daniela; Methuku, Abhishek; Osthus, Deryk
摘要：The Erdo ˝s-Faber-Lovasz conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on n vertices is at most n. In this paper, we prove this conjecture for every large n. We also provide stability versions of this result, which confirm a prediction of Kahn.
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作者：Keel, Sean; Yu, Tony yue
摘要：Let U be an affine log Calabi-Yau variety containing an open algebraic torus. We show that the naive counts of rational curves in U uniquely determine a commutative associative algebra equipped with a compatible multilinear form. This proves a variant of the Frobenius structure conjecture by Gross-Hacking-Keel in mirror symmetry, and the spectrum of this algebra is supposed to give the hypothetical mirror family. Although the statement of our theorem involves only elementary algebraic geometry...
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作者：Matomaeki, Kaisa; Radziwill, Maksym; Tao, Terence; Teraevaeinen, Joni; Ziegler, Tamar
摘要：Let lambda denote the Liouville function. We show that, as X-+ oo,2X Zsup X P(Y)ER[Y] degP 0 < theta < 1 fiixed but arbitrarily small. Previously this was only established for k < 1. We obtain this result as a special case of the corresponding statement for (non-pretentious) 1 -bounded multiplicative functions that we prove.In fact, we are able to replace the polynomial phases e(-P (n)) by degree k nilsequences F(g(n)Gamma). By the inverse theory for the Gowers norms this implies the higher or...
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作者：Yuan, Xinyi; Zhang, Shou-Wu
摘要：We will fix an error in our paper on the average Colmez conjecture by proving a slightly weaker statement than Theorem 2.7, which is sufficient for application to the main results.
