# Rigid cohomology over Laurent series field I: First definitions and basic properties

@article{Lazda2014RigidCO, title={Rigid cohomology over Laurent series field I: First definitions and basic properties}, author={Christopher Lazda and Ambrus P'al}, journal={arXiv: Number Theory}, year={2014} }

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 $\mathcal{E}_K^\dagger$, 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…

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