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作者：Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho
作者单位：United Arab Emirates University; Kyoto University; Korea Institute for Advanced Study (KIAS); Kyung Hee University
摘要：We fix a mistake in [1] on the definition of commuting family of central objects.
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作者：Antieau, Benjamin; Gepner, David; Heller, Jeremiah
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Melbourne; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree -1. The main results of this paper are that K-1(E) vanishes when E is a small stable -category with a bounded t-structure and that K-n(E) vanishes for all n1 when additionally the heart of E is noetherian. It follows that Barwick's theorem of the heart holds for nonconnective K-theory spectra when the heart is noetheria...
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作者：Sasaki, Shu
作者单位：University of Duisburg Essen
摘要：We prove the strong Artin conjecture for continuous, totally odd, two-dimensional representations of the absolute Galois group of a totally real field F.
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作者：Arakawa, Tomoyuki; Creutzig, Thomas; Linshaw, Andrew R.
作者单位：Kyoto University; University of Alberta; University of Denver
摘要：We prove the long-standing conjecture on the coset construction of the minimal series principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's conjecture on the coset realization of the universal principal W-algebras, which are not necessarily simple. As consequences, the unitarity of the discrete series of principal W-algebras is established, a second coset realization of rational and unitary W-algebras of type A and D are given and the rationality of Ka...
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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.
