-
作者：Bryant, J.; Ferry, S.; Mio, W.; Weinberger, S.
-
作者：Kusakabe, Yuta
摘要：Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold. This gives a positive answer to the well-known long-standing problem in Oka theory whether the complement of a compact polynomially convex set in Cn (n > 1) is Oka. Furthermore, we obtain new examples of non -elliptic Oka manifolds which negatively answer Gromov's question. The relative version of the main theorem is also proved. As an applicatio...
-
作者：Mattheus, Sam; Verstraete, Jacques
摘要：For integers s, t >= 2, the Ramsey number r(s, t) denotes the minimum n such that every n-vertex graph contains a clique of order s or an independent set of order t. In this paper we prove r(4, t) = Omega (t(3)/log(4)t) as t -> infinity, which determines r(4, t) up to a factor of order log(2)t, and solves a conjecture of Erdos.
-
作者：Caraiani, Ana; Scholze, Peter
摘要：We prove that the generic part of the mod $ cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, extending our previous work to a noncompact case. The result applies even to Eisenstein cohomology classes coming from the locally symmetric space of the general linear group, and has been used in joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Taylor and Thorne to get good control on these classes and deduc...
