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作者：Ancona, Giuseppe
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Let A be an abelian fourfold in characteristic p. We prove the standard conjecture of Hodge type for A, namely that the intersection product Z(num)(2)(A)(Q) x Z(num)(2) (A)(Q) -> Q is of signature (rho(2) - rho(1) + 1; rho(1) - 1), with rho(n) = dim Z(num)(n)(A)(Q). (Equivalently, it is positive definite when restricted to primitive classes for any choice of the polarization.) The approach consists in reformulating this question into a p-adic problem and then using p-adic Hodge theory to solve...
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作者：Looper, Nicole R.
作者单位：Brown University
摘要：We address the Uniform Boundedness Conjecture of Morton and Silverman in the case of unicritical polynomials, assuming a generalization of the abc-conjecture. For unicritical polynomials of degree at least five, we require only the standard abc-conjecture.
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作者：Bezrukavnikov, Roman; Vilonen, Kari
作者单位：Massachusetts Institute of Technology (MIT); University of Melbourne; University of Helsinki
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作者：Zhuang, Ziquan
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We give an algebraic proof of the equivalence of equivariant K-semistability (resp. equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability). Along the way we also prove the existence and uniqueness of minimal optimal destabilizing centers on K-unstable log Fano pairs.
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作者：Budur, Nero; van der Veer, Robin; Wu, Lei; Zhou, Peng
作者单位：KU Leuven; Utah System of Higher Education; University of Utah; Universite Paris Saclay
摘要：We prove a conjecture of the first author relating the Bernstein-Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This generalizes a classical theorem of Malgrange and Kashiwara relating the b-function of a multivariate polynomial with the monodromy eigenvalues on the Milnor fibers cohomology.
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作者：Hedden, Matthew; Pinzon-Caicedo, Juanita
作者单位：Michigan State University; University of Notre Dame
摘要：We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank subgroup of the smooth concordance group C. Our criterion applies widely; notably to many unknotted patterns for which the corresponding operators on the topological concordance gro...
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作者：Karpukhin, Mikhail
作者单位：University of California System; University of California Irvine
摘要：In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres Sn. First, we propose a new approach to isoperimetric eigenvalue inequalities based on energy index. Using this approach we show that for any positive k, the k-th non-zero eigenvalue of the Laplacian on the real projective plane endowed with a metric of unit area, is maximized on the sequence of metrics converging to a union of (k - 1) identical copies of round ...
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作者：Sawin, Will
作者单位：Columbia University
摘要：We prove a characteristicpanalogue of a result of Massey which bounds the dimensions of the stalks of a perverse sheaf in terms of certain intersection multiplicities of the characteristic cycle of that sheaf. This uses the construction of the characteristic cycle of a perverse sheaf in characteristicpby Saito. We apply this to prove a conjecture of Shende and Tsimerman on the Betti numbers of the intersections of two translates of theta loci in a hyperelliptic Jacobian. This implies a functio...
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作者：Heuer, Nicolaus; Loeh, Clara
作者单位：University of Cambridge; University of Regensburg
摘要：New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds is dense in R->= 0. In dimension 4 we prove that every non-negative rational number is the simplicial volume of some orientable closed connected 4-manifold. Our group theoretic results relate stable commutator length to the l(1)-semi-norm of certain singula...
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作者：Cavalletti, Fabio; Milman, Emanuel
作者单位：International School for Advanced Studies (SISSA); Technion Israel Institute of Technology
摘要：The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for ametric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition locally: an essentially non-branching metric-measure space (X, d, m) (so that (supp(m), d) is a length-space and m( X) < infinity) verifying the local Curvature-Dimension condition CDloc( K, N) with parameters K is an element of R and N is an element of(1, infin...
