2014/11/25 by Lazda, Christopher, Pál, Ambrus
#11G20 #14F30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1411.7000
This is the first in a series of papers in which we construct and study a new p-adic cohomology theory for varieties over Laurent series fields k( (t) ) in characteristic p. This will be a version of rigid cohomology, taking values in the bounded Robba ring EK^†, and in this paper, we give the basic definitions and constructions. The cohomology theory we define can be viewed as a relative version of Berthelot's rigid cohomology, and is constructed by compactifying k( (t) )-varieties as schemes over k[ [ t] ] rather than over k( (t) ). We reprove the foundational results necessary in our new context to show that the theory is well defined and functorial, and we also introduce a category of `twisted' coefficients. In latter papers we will show some basic structural properties of this theory, as well as discussing some arithmetic applications including the weight monodromy conjecture and independence of ℓ results for equicharacteristic local fields.