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作者：Pop, Florian
作者单位：University of Pennsylvania
摘要：In this note we introduce and prove a wide generalization and sharpening of Ihara's question/Oda-Matsumoto conjecture, for short I/OM. That leads to a quite concrete topological/combinatorial description of absolute Galois groups, in particular of Gal(Q)=Aut((Q) over bar), as envisioned by Grothendieck in his Esquisse d'un Programme.
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作者：Rizzardo, Alice; Van den Bergh, Michel; Neeman, Amnon
作者单位：University of Edinburgh; Hasselt University; Australian National University
摘要：Orlov's famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. In this paper we show that this result is false without the fully faithfulness hypothesis. We also show that our functor does not lift to the homotopy category of spectral categories if the ground field is Q.
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作者：Szymik, Markus; Wahl, Nathalie
作者单位：Norwegian University of Science & Technology (NTNU); University of Copenhagen
摘要：We prove that Thompson's group V is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman-Thompson groups V-n,V-r with the homology of the zeroth component of the infinite loop space of the mod n - 1 Moore spectrum. As V = V-2,V-1, we can deduce that this group is acyclic. Our proof involves establishing homological stability with respect to r, as well as a computation of the algebraic K-theory of the category of finitely generated ...
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作者：Eskin, Alex; Mirzakhani, Maryam; Rafi, Kasra
作者单位：University of Chicago; Stanford University; University of Toronto
摘要：We compute the asymptotic growth rate of the number N(C,R) of closed geodesics of length R in a connected component C of a stratum of quadratic differentials. We prove that, for any 01, the number of closed geodesics of length at most R such that spends at least -fraction of its time outside of a compact subset of C is exponentially smaller than N(C,R). The theorem follows from a lattice counting statement. For points x,y in the moduli space M(S) of Riemann surfaces, and for 01 we find an uppe...
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作者：Bousseau, Pierrick
作者单位：Imperial College London
摘要：Block and Gottsche have defined a q-number refinement of counts of tropical curves in R2. Under the change of variables q=eiu, we show that the result is a generating series of higher genus log Gromov-Witten invariants with insertion of a lambda class. This gives a geometric interpretation of the Block-Gottsche invariants and makes their deformation invariance manifest.
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作者：Waldron, Alex
摘要：We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter et al. (Am J Math 120:117-128, 1998). The proof relies on a weighted energy identity and sharp decay estimates in the neck region.
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作者：Dahmani, Francois; Touikan, Nicholas
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of New Brunswick
摘要：We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups) by congruences, and the mixed Whitehead problem, an automorphism group orbit problem. The first step of the reduction is to compute canonical JSJ decompositions. Dehn fillings ...
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作者：Erman, Daniel; Sam, Steven V.; Snowden, Andrew
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California San Diego; University of Michigan System; University of Michigan
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作者：Li, Chunyi
作者单位：University of Warwick
摘要：We study the Clifford type inequality for a particular type of curves C-2,C-2,C-5, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macri, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in P-C(4).
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作者：Skipper, Rachel; Witzel, Stefan; Zaremsky, Matthew C. B.
作者单位：University of Gottingen; University of Bielefeld; State University of New York (SUNY) System; University at Albany, SUNY
摘要：We show that for every positive integer n there exists a simple group that is of type Fn-1 but not of type Fn. For n3 these groups are the first known examples of this kind. They also provide infinitely many quasi-isometry classes of finitely presented simple groups. The only previously known infinite family of such classes, due to Caprace-Remy, consists of non-affine Kac-Moody groups over finite fields. Our examples arise from Rover-Nekrashevych groups, and contain free abelian groups of infi...
