2014/12/17 by Christopher Lazda, Lazda, Christopher, Ambrus Pál +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1412.5300
In this paper we prove that the E^†K-valued cohomology, introduced in [9] is finite dimensional for smooth curves over Laurent series fields k((t)) in positive characteristic, and forms an E^†K-lattice inside `classical' EK-valued rigid cohomology. We do so by proving a suitable version of the p-adic local monodromy theory over E^†K, and then using an étale pushforward for smooth curves to reduce to the case of \mathbbA1. We then introduce E^†K-valued cohomology with compact supports, and again prove that for smooth curves, this is finite dimensional and forms an E^†K-lattice in EK-valued cohomology with compact supports. Finally, we prove Poincaré duality for smooth curves, but with restrictions on the coefficients.