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作者：Chiodo, Alessandro; Eisenbud, David; Farkas, Gavril; Schreyer, Frank-Olaf
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of California System; University of California Berkeley; Humboldt University of Berlin; Saarland University
摘要：We formulate, and in some cases prove, three statements concerning the purity or, more generally, the naturality of the resolution of various modules one can attach to a generic curve of genus g and a torsion point of a in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space of twisted level a curves of genus g and us...
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作者：Mendel, Manor; Naor, Assaf
作者单位：Open University Israel; New York University; Microsoft; University of Washington; University of Washington Seattle
摘要：It is shown that for every epsilon a(0,1), every compact metric space (X,d) has a compact subset SaS dagger X that embeds into an ultrametric space with distortion O(1/epsilon), and dim(H) (S) >= (1 - epsilon) dim(H) (X), where dim (H) (.) denotes Hausdorff dimension. The above O(1/epsilon) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.
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作者：Gaitsgory, Dennis
作者单位：Harvard University
摘要：We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space of G-bundles on X is uniformized by the appropriate rational version of the affine Grassmannian, where the uniformizing map has contractible fibers.
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作者：Behrend, Kai; Bryan, Jim; Szendroi, Balazs
作者单位：University of British Columbia; University of Oxford
摘要：Given a smooth complex threefold X, we define the virtual motive of the Hilbert scheme of n points on X. In the case when X is Calabi-Yau, gives a motivic refinement of the n-point degree zero Donaldson-Thomas invariant of X. The key example is X=a,(3), where the Hilbert scheme can be expressed as the critical locus of a regular function on a smooth variety, and its virtual motive is defined in terms of the Denef-Loeser motivic nearby fiber. A crucial technical result asserts that if a functio...
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作者：Brudnyi, Alexander
作者单位：University of Calgary
摘要：We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H (a) of bounded holomorphic functions on the unit disk with pointwise multiplication and supremum norm. In particular, we establish vanishing cohomology for sheaves of germs of such functions and, solving a Banach-valued corona problem for H (a), prove that the maximal ideal space of the algebra of holomorphic functions on with relatively compact images in a commutative unital...
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作者：Hida, Haruzo
作者单位：University of California System; University of California Los Angeles
摘要：Let pa parts per thousand yen5 be a prime. If an irreducible component of the spectrum of the 'big' ordinary Hecke algebra does not have complex multiplication, under mild assumptions, we prove that the image of its mod p Galois representation contains an open subgroup of for the canonical weight variable T. This fact appears to be deep, as it is almost equivalent to the vanishing of the mu-invariant of the Kubota-Leopoldt p-adic L-function and the anticyclotomic Katz p-adic L-function. Anothe...
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作者：Blocki, Zbigniew
作者单位：Jagiellonian University
摘要：We prove a conjecture of N. Suita which says that for any bounded domain D in a, one has , where c (D) (z) is the logarithmic capacity of a,a-D with respect to zaD and K (D) the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.
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作者：Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
作者单位：University of Cambridge; University of Jyvaskyla; University of Washington; University of Washington Seattle; University of California System; University of California Irvine
摘要：We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.
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作者：Pappas, G.; Zhu, X.
作者单位：Michigan State University; Northwestern University
摘要：We give a group theoretic definition of local models as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a p-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixe...
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作者：Mischler, Stephane; Mouhot, Clement
作者单位：Universite PSL; Universite Paris-Dauphine; University of Cambridge
摘要：This paper is devoted to the study of propagation of chaos and mean-field limits for systems of indistinguishable particles, undergoing collision processes. The prime examples we will consider are the many-particle jump processes of Kac and McKean (Kac in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954-1955, Vol. III, pp. 171-197, 1956; McKean in J. Comb. Theory 2:358-382, 1967) giving rise to the Boltzmann equation. We solve the conjecture raised b...
