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作者：Leslie, Spencer
摘要：We prove the endoscopic fundamental lemma for the Lie algebra of the symmetric variety U(2n)/U(n) x U(n), where U(n) denotes a unitary group of rank n. This is the first major step in the stabilization of the relative trace formula associated to the U(n) x U(n)-periods of automorphic forms on U(2n).
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作者：Zavyalov, Bogdan
摘要：We show Poincare Duality for Fp-etale cohomology of a smooth proper rigid-analytic space over a non-archimedean field K of mixed characteristic (0, p). It positively answers the question raised by P. Scholze in his paper p-adic Hodge theory for rigid-analytic varieties. We prove duality via constructing Faltings' trace map relating Poincare Duality on the generic fiber to (almost) Grothendieck Duality on the mod-p fiber of a formal model. We also formally deduce Poincare Duality for Z/pnZ, Zp,...
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作者：An, Xinliang
摘要：Employing the Einstein-scalar field system, we demonstrate an approach for proving high co-dimensional nonlinear instability of naked-singularity solutions as constructed by Christodoulou in 1994. We further investigate the censorship of Christodoulou's naked singularity and show that a tiny anisotropic perturbation arising from the outgoing characteristic initial data would lead to the emergence of an anisotropic apparent horizon, which covers and censors the naked singularity. Our approach a...
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作者：Jaikin-Zapirain, Andrei; Linton, Marco
摘要：We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two complexes with non-positive immersions are homologically coherent, we show that groups with staggered presentations and many Coxeter groups are coherent and we show that group algebras over fields of characteristic zero of groups with reducible presentations with...
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作者：Jaikin-Zapirain, Andrei; Linton, Marco
作者单位：Autonomous University of Madrid; Universidad Carlos III de Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Universidad Carlos III de Madrid; Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT)
摘要：We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two complexes with non-positive immersions are homologically coherent, we show that groups with staggered presentations and many Coxeter groups are coherent and we show that group algebras over fields of characteristic zero of groups with reducible presentations with...
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作者：Jaikin-Zapirain, Andrei; Linton, Marco
作者单位：Autonomous University of Madrid; Universidad Carlos III de Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Universidad Carlos III de Madrid; Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT)
摘要：We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two complexes with non-positive immersions are homologically coherent, we show that groups with staggered presentations and many Coxeter groups are coherent and we show that group algebras over fields of characteristic zero of groups with reducible presentations with...
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作者：An, Xinliang
作者单位：National University of Singapore
摘要：Employing the Einstein-scalar field system, we demonstrate an approach for proving high co-dimensional nonlinear instability of naked-singularity solutions as constructed by Christodoulou in 1994. We further investigate the censorship of Christodoulou's naked singularity and show that a tiny anisotropic perturbation arising from the outgoing characteristic initial data would lead to the emergence of an anisotropic apparent horizon, which covers and censors the naked singularity. Our approach a...
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作者：Kisin, Mark; Zhou, Bong
作者单位：Harvard University; University of Cambridge
摘要：Let A be an abelian variety over a number field E subset of C, and let G denote the Mumford-Tate group of A. After replacing E by a finite extension, the action of the absolute Galois group Gal(E/E) on the & ell;-adic cohomology H1et(AE, Q & ell;) factors through G(Q & ell;). We show that for v an odd prime of E where A has good reduction, the conjugacy class of Frobenius Frobvin G(Q & ell;) is independent of & ell;. Along the way, we prove that under certain hypotheses, every point in the mu ...
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作者：Leslie, Spencer
作者单位：Boston College
摘要：We prove the endoscopic fundamental lemma for the Lie algebra of the symmetric variety U(2n)/U(n) x U(n), where U(n) denotes a unitary group of rank n. This is the first major step in the stabilization of the relative trace formula associated to the U(n) x U(n)-periods of automorphic forms on U(2n).
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作者：Lawrence, Brian; Sawin, Will
作者单位：Princeton University
摘要：Faltings proved that there are finitely many abelian varieties of genus g over a number field K, with good reduction outside a finite set of primes S. Fixing one of these abelian varieties A, we prove that there are finitely many smooth hypersurfaces in A, with good reduction outside S, representing a given ample class in the Neron-Severi group of A, up to translation, as long as the dimension of A is at least four. Our approach builds on the approach of Lawrence and Venkatesh, which studies p...
