SURJECTIVITY OF p-ADIC REGULATOR ON K2 OF TATE CURVES
نویسندگان
چکیده
from Quillen’s K-groups to the étale cohomology groups with coefficients in the Tate twist Zp(j) ([8], [25]). When K is a local field, it is a long-standing problem whether the maps Ki(X) ⊗ Qp → H ét (X,Qp(j)) for 2j > i are surjective, in relation to the Beilinson conjectures (cf. [11] §3). The main result of this paper is to give an affirmative answer to this problem for K2 of the Tate curves over certain p-adic fields: Theorem 1.1. Let K be a finite extension of Qp. Let EK = K /q be the Tate curve over K where q ∈ K is a non-zero element with its order ord(q) > 0. Suppose that K ⊂ Qp(ζ) for some root of unity ζ. Then the p-adic regulator K2(EK)⊗Qp −→ H ét(EK ,Qp(2)) (1.2)
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تاریخ انتشار 2005