We show that the existence of rational points on smooth varieties over a field can be detected using homotopy fixed points of étale topological types under the Galois action. As our main example we show that the surjectivity statement in Grothendieck’s Section Conjecture would follow from the surjectivity of the map from fixed points to continuous homotopy fixed points on the level of connected...

The three-dimensional case is the most difficult one. A version of Theorem 1.1 is known for a long time for the circle (see [Cra] and [Lan1]) and for the d-dimensional ball when d ≥ 4 (see [Wal]). In [Ble1] a similar statement was proved for any strictly convex (in the sense that the curvature of the boundary is positive everywhere) oval in the plane with the origin inside the oval. Making an a...

autoimmune hepatitis is a chronic hepatitis that occurs in children and adults of all ages. diagnosis is based upon characteristic serologic and histologic findings and the exclusion of other forms of chronic liver disease. guidelines issued by the aasld suggest the following diagnostic considerations: the diagnosis should be made in patients with compatible clinical signs, symptoms, and labora...

whenever a belongs to the closed convex hull of the set of weak limit points of {an}∞n=1. In case X has the Banach-Saks property and {an}∞n=1 is bounded the converse assertion holds too. A characterization of reflexive spaces in terms of limit points and cores of bounded sequences is also given. The motivation for the problems investigated goes back to Lévy laplacian from potential theory in Hi...

Let G be a non-elementary word-hyperbolic group acting as a convergence group on a compact metrizable space Z so that there exists a continuous G-equivariant map i : ∂G → Z, which we call a Cannon-Thurston map. We obtain two characterizations (a dynamical one and a geometric one) of conical limit points in Z in terms of their pre-images under the CannonThurston map i. As an application we prove...