On Families of Pure Slope L-Functions
نویسندگان
چکیده
Let R be the ring of integers in a finite extension K of Qp, let k be its residue field and let χ : π1(X) → R× = GL1(R) be a ”geometric” rank one representation of the arithmetic fundamental group of a smooth affine k-scheme X. We show that the locally Kanalytic characters κ : R× → Cp are the Cp-valued points of a K-rigid space W and that L(κ ◦ χ, T ) = ∏ x∈X 1 1− (κ ◦ χ)(Frobx)T deg(x) , viewed as a two variable function in T and κ, is meromorphic on A1Cp × W. On the way we prove, based on a construction of Wan, a slope decomposition for ordinary overconvergent (finite rank) σmodules, in the Grothendieck group of nuclear σ-modules. 2000 Mathematics Subject Classification: Primary 14F30; Secondary 14G10, 14G13, 14G15, 14G22
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