On families of pure slope -functions
Elmar Grosse-Klönne
![On families of pure slope $L$-functions cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-8.png&w=3840&q=90)
Abstract
Let be the ring of integers in a finite extension of , let be its residue field and let be a “geometric” rank one representation of the arithmetic fundamental group of a smooth affine -scheme . We show that the locally -analytic characters are the -valued points of a -rigid space and that
viewed as a two variable function in and , is meromorphic on . On the way we prove, based on a construction of Wan, a slope decomposition for ordinary overconvergent (finite rank) -modules, in the Grothendieck group of nuclear -modules.
Cite this article
Elmar Grosse-Klönne, On families of pure slope -functions. Doc. Math. 8 (2003), pp. 1–42
DOI 10.4171/DM/135