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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：Izumi, Masaki; Matui, Hiroki
作者单位：Kyoto University; Chiba University
摘要：This is the second part of our serial work on the classification of poly-Z group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of continuous fields of Kirchberg algebras over the classifying spaces. As an application, we determine the number of cocycle conjugacy classes of outer Z(n)-actions on the Cuntz algebras.
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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：Clausen, Dustin; Mathew, Akhil
作者单位：University of Copenhagen; University of Chicago
摘要：We study the etale sheafification of algebraic K-theory, called etale K-theory. Our main results show that etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories. Consequently, we show that etale K-theory has surprisingly well-behaved properties, integrally and without finiteness assumptions. A key theoretical ingredient is the distinction, which we investigate in detail, between sheaves and hypersheaves of spectra on etal...
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作者：Brendle, Simon; Daskalopoulos, Panagiota; Sesum, Natasa
作者单位：Columbia University; Rutgers University System; Rutgers University New Brunswick
摘要：In this paper, we study the classification of kappa-noncollapsed ancient solutions to three-dimensional Ricci flow on S-3. We prove that such a solution is either isometric to a family of shrinking round spheres, or the Type II ancient solution constructed by Perelman.
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作者：Huang, Jingyin; Osajda, Damian
作者单位：University System of Ohio; Ohio State University; University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular, such groups act geometrically on spaces with a convex geodesic bicombing, equipping them with a nonpositive-curvature-like structure. That structure has many properties of a CAT(0) structure and, additionally, it has a combinatorial flavor imp...
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作者：Cascini, Paolo; Spicer, Calum
作者单位：Imperial College London
摘要：We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a Q-factorial projective threefold. As applications, we show the existence of F-dlt modifications and F-terminalisations for foliated pairs and we show that foliations with canonical or F-dlt singularities admit non-dicritical singularities. Finally, we show abundance in the case of numerically trivial fol...
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作者：Bell, Jason; Zelmanov, Efim
作者单位：University of Waterloo; University of California System; University of California San Diego
摘要：We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
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作者：Kemeny, Michael
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We introduce a relativization of the secant sheaves from Green and Lazarsfeld (A simple proof of Petri's theorem on canonical curves, Geometry Today, 1984) and Ein and Lazarsfeld (Inventiones Math 190:603-646, 2012) and apply this construction to the study of syzygies of canonical curves. As a first application, we give a simpler proof of Voisin's Theorem for general canonical curves. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves. Sec...
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作者：Dougall, Rhiannon; Sharp, Richard
作者单位：University of Bristol; University of Warwick
摘要：The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions seen, for example, in the work of Stadlbauer on symmetric group extensions and of the authors on geodesic flows. Our main application is to growth rates of periodic orbits for covers of an Anosov flow: we reduce the problem of counting periodic orbits in an amenable cover X to counting in a maximal abelian subcover ...
