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作者：Kings, Guido; Sprang, Johannes
作者单位：University of Regensburg; University of Duisburg Essen
摘要：We show that for an arbitrary totally complex number field L the (regularized) critical L-values of algebraic Hecke characters of L divided by certain periods are algebraic integers. This relies on a new construction of an equivariant coherent cohomology class with values in the completion of the Poincare bundle on an abelian scheme A. From this we obtain a cohomology class for the automorphism group of a CM abelian scheme A with values in some canonical bundles, which can be explicitly calcul...
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作者：Zavyalov, Bogdan
作者单位：Princeton University; Institute for Advanced Study - USA
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：Giri, Vikram; Kwon, Hyunju; Novack, Matthew
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich; Purdue University System; Purdue University
摘要：In this work, we prove the L-3-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to C-t(0)(W-1/3-,W-3 boolean AND L infinity-). More precisely, for every beta < 1/3, we can construct such solutions in the space C-t(0)(B-3,infinity(beta) boolean AND 1/L1-3 beta).
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作者：Nelson, Paul d.
作者单位：Aarhus University
摘要：We determine the asymptotic quantum variance of microlo cal lifts of Hecke-Maass cusp forms on the arithmetic compact hyperbolic surfaces attached to maximal orders in quaternion algebras. Our result extends those for the non-compact modular surface obtained by Luo-Sarnak-Zhao, whose method required a cusp. The global arguments in our proof involve an analytic study of the theta correspondence, the interplay between additive and multiplicative harmonic analysis on quaternion algebras, the equi...
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作者：Calmes, Baptiste; Dotto, Emanuele; Harpaz, Yonatan; Hebestreit, Fabian; Land, Markus; Moi, Kristian; Nardin, Denis; Nikolaus, Thomas; Steimle, Wolfgang
作者单位：Universite d'Artois; University of Warwick; Sorbonne Universite; Universite Paris Cite; University of Bielefeld; Johannes Gutenberg University of Mainz; Royal Institute of Technology; University of Regensburg; University of Munster; University of Augsburg
摘要：We establish a fibre sequence relating the classical Grothendieck-Witt theory of a ring R to the homotopy C-2-orbits of its K-theory and Ranicki's original (non-periodic) symmetric L-theory. We use this fibre sequence to remove the assumption that 2 is a unit in R from various results about Grothendieck-Witt groups. For instance, we solve the homotopy limit problem for Dedekind rings whose fraction field is a number field, calculate the various flavours of Grothendieck-Witt groups of Z, show t...
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作者：Guth, Larry; Maynard, James
作者单位：Massachusetts Institute of Technology (MIT); University of Oxford; University of Oxford
摘要：We prove new bounds for how often Dirichlet polynomials can take large values. This gives improved estimates for a Dirichlet polynomial of length N taking values of size close to N3/4, which is the critical situation for several estimates in analytic number theory connected to prime numbers and the Riemann zeta function. As a consequence, we deduce a zero density estimate N(sigma, T) <= T30(1-sigma )/13+o(1) and asymptotics for primes in short intervals of length x17/30+o(1).
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作者：Prasad, Gopal
作者单位：University of Michigan System; University of Michigan
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作者：Campos, Marcelo; Griffiths, Simon; Morris, Robert; Sahasrabudhe, Julian
摘要：The Ramsey number R(k) is the minimum n is an element of N such that every red-blue colouring of the edges of the complete graph Kn on n vertices contains a monochromatic copy of K-k. We prove that R(k) <= (4-epsilon)(k) for some constant epsilon > 0. This is the first exponential improvement over the upper bound of Erdos and Szekeres, proved in 1935.
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作者：Chodosh, Otis; Li, Chao; Minter, Paul; Stryker, Douglas
作者单位：Stanford University; New York University; Princeton University; Institute for Advanced Study - USA; University of Cambridge
摘要：We show that a complete, two-sided stable minimal hypersurface in R5 is flat.
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作者：Brue, Elia; Naber, Aaron; Semola, Daniele
作者单位：Bocconi University; Northwestern University; Institute for Advanced Study - USA; Princeton University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Vienna
摘要：It was conjectured by Milnor in 1968 that the fundamental group of a complete manifold with nonnegative Ricci curvature is finitely generated. The main result of this paper is a counterexample, which provides an example M-7 with Ric >= 0 such that pi 1(M) = Q/Z is infinitely generated. There are several new points behind the result. The first is a new topological construction for building manifolds with infinitely generated fundamental groups, which can be interpreted as a smooth version of th...
