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作者：Evertse, J-H.; Ferretti, R. G.
摘要：In 2002, Evertse and Schlickewei obtained a quantitative version of the so-called Absolute Parametric Subspace Theorem. This result deals with a parametrized class of twisted heights. One of the consequences of this result is a quantitative version of the Absolute Subspace Theorem, giving an explicit upper bound for the number of subspaces containing the solutions of the Diophantine inequality under consideration. In the present paper, we further improve Evertse's and Schlickewei's quantitativ...
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作者：Dimca, Alexandru; Papadima, Stefan
摘要：We examine groups whose resonance varieties, characteristic varieties and Sigma-invariants have a natural arithmetic group symmetry, and we explore implications on various finiteness properties of subgroups. We compute resonance varieties, characteristic varieties and Alexander polynomials of Torelli groups, and we show that all subgroups containing the Johnson kernel have finite first Betti number, when the genus is at least 4. We also prove that, in this range, the I-adic completion of the A...
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作者：Hacon, Christopher D.; McKernan, James; Xu, Chenyang
摘要：We show that the number of birational automorphisms of a variety of general type X is bounded by c . vol(X,Kx), where c is a constant that only depends on the dimension of X.
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作者：Kessar, Radha; Malle, Gunter
摘要：This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-called quasi-isolated blocks of exceptional groups of Lie type for bad primes. This relies on the explicit decomposition of Lusztig induction from suitable Levi subgroups. Our second major result is the proof of one direction of Brauer's long-standing height zero conjecture on blocks of finite groups, using the reduction by Berger and Knorr to the quasi-simp...
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作者：Bennett, Michael A.; Dahmen, Sander R.
摘要：If F(x, y) is an element of Z[x, y] is an irreducible binary form of degree k >= 3, then a theorem of Darmon and Granville implies that the generalized superelliptic equation F(x, y) = z(l) has, given an integer l >= max{2, 7 - k}, at most finitely many solutions in coprime integers x, y and z. In this paper, for large classes of forms of degree k = 3, 4, 6 and 12 (including, heuristically, most cubic forms), we extend this to prove a like result, where the parameter l is now taken to be varia...
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作者：Miyaoka, Reiko
摘要：We prove that isoparametric hypersurfaces with (g,m) = (6,2) are homogeneous, which answers Dorfmeister-Nehers conjecture affirmatively and solves Yaus problem in the case g=6.
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作者：Krishnapur, Manjunath; Kurlberg, Par; Wigman, Igor
摘要：Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus (arithmetic random waves). We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is nonuniversal. Our result is intimately related to the arithmetic of lattice points lying on a circle with r...
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作者：Castro, Angel; Cordoba, Diego; Fefferman, Charles; Gancedo, Francisco; Gomez-Serrano, Javier
摘要：In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem) for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.
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作者：Deligne, Pierre; Flicker, Yuval Z.
摘要：Let X-1 be a curve of genus g, projective and smooth over F-q. Let S-1 subset of X-1 be a reduced divisor consisting of N-1 closed points of X-1. Let (X, S) be obtained from (X-1, S-1) by extension of scalars to an algebraic closure F of F-q. Fix a prime l not dividing q. The pullback by the Frobenius endomorphism Fr of X induces a permutation Fr* of the set of isomorphism classes of rank n irreducible (Q(l)) over bar -local systems on X - S. It maps to itself the subset of those classes for w...
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作者：Navarro, Gabriel; Pham Huu Tiep
摘要：Let Z be a normal subgroup of a finite group G, let lambda is an element of Irr(Z) be an irreducible complex character of Z, and let p be a prime number. If p does not divide the integers chi(1)/lambda(1) for all chi is an element of Irr(G) lying over lambda, then we prove that the Sylow p-subgroups of G/Z are abelian. This theorem, which generalizes the Gluck-Wolf Theorem to arbitrary finite groups, is one of the principal obstacles to proving the celebrated Brauer Height Zero Conjecture.
