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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：Eichmair, Michael; Metzger, Jan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Potsdam
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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：White, Brian
作者单位：Stanford University
摘要：Consider the mean curvature flow of an (n+1)-dimensional compact, mean convex region in Euclidean space (or, if n < 7, in a Riemannian manifold). We prove that elements of the mth homotopy group of the complementary region can die only if there is a shrinking S (k) xR (n-k) singularity for some ka parts per thousand currency signm. We also prove that for each m with 1a parts per thousand currency signma parts per thousand currency signn, there is a nonempty open set of compact, mean convex reg...
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作者：Kobayashi, Shinichi
作者单位：Tohoku University
摘要：Let p be a prime number and let E be an elliptic curve defined over ae of conductor N. Let K be an imaginary quadratic field with discriminant prime to pN such that all prime factors of N split in K. B. Perrin-Riou established the p-adic Gross-Zagier formula that relates the first derivative of the p-adic L-function of E over K to the p-adic height of the Heegner point for K when E has good ordinary reduction at p. In this article, we prove the p-adic Gross-Zagier formula of E for the cyclotom...
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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：Poineau, Jerome
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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：Gabber, Ofer; Liu, Qing; Lorenzini, Dino
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; University System of Georgia; University of Georgia
摘要：Let K be the field of fractions of a Henselian discrete valuation ring . Let X (K) /K be a smooth proper geometrically connected scheme admitting a regular model . We show that the index delta(X (K) /K) of X (K) /K can be explicitly computed using data pertaining only to the special fiber X (k) /k of the model X. We give two proofs of this theorem, using two moving lemmas. One moving lemma pertains to horizontal 1-cycles on a regular projective scheme X over the spectrum of a semi-local Dedeki...
