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- W1700698168 abstract "In this paper we investigate the arithmetic aspects of the theory of $mathcal{E}_K^dagger$-valued rigid cohomology introduced and studied in [11,12]. In particular we show that these cohomology groups have compatible connections and Frobenius structures, and therefore are naturally $(varphi,nabla)$-modules over $mathcal{E}_K^dagger$ whenever they are finite dimensional. We also introduce a category of `absolute' coefficients for the theory; the same results are true for cohomology groups with coefficients. We moreover prove a $p$-adic version of the weight monodromy conjecture for smooth (not necessarily proper) curves, and use a construction of Marmora to prove a version of $ell$-independence for smooth curves over $k(!(t)!)$ that includes the case $ell=p$. This states that after tensoring with $mathcal{R}_K$, our $p$-adic cohomology groups agree with the $ell$-adic Galois representations $H^i_{mathrm{et}}(X_{k(!(t)!)^mathrm{sep}},mathbb{Q}_ell)$ for $ellneq p$." @default.
- W1700698168 created "2016-06-24" @default.
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- W1700698168 date "2015-03-09" @default.
- W1700698168 modified "2023-09-27" @default.
- W1700698168 title "Rigid cohomology over Laurent series fields III: Absolute coefficients and arithmetic applications" @default.
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