PICARD GROUPS IN p-ADIC FOURIER THEORY
نویسنده
چکیده
Let L 6= Qp be a proper finite field extension of Qp and o ⊂ L its ring of integers viewed as an abelian locally L-analytic group. Let ô be the rigid L-analytic group parametrizing the locally analytic characters of o constructed by Schneider-Teitelbaum. Let K/L be a finite extension field. We show that the base change ôK has a Picard group Pic(ôK) which is profinite and that the unit section in ôK provides a divisor class of infinite order. In particular, the abelian group Pic(ôK) is not finitely generated and is not a torsion group. On the way we show that ôK is a nontrivial étale covering of the affine line over K realized via the logarithm map of a Lubin-Tate formal group. We finally prove that rank and determinant mappings induce an isomorphism between K0(ôK) and Z⊕ Pic(ôK).
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