Publications of the Research Institute for Mathematical Sciences
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Published online: 2010-06-07
On the Kernel and the Image of the Rigid Analytic Regulator in Positive CharacteristicAmbrus Pál (1) Imperial College, London, UK
We will formulate and prove a certain reciprocity law relating certain residues of the diﬀerential symbol dlog2 from the K2 of a Mumford curve to the rigid analytic regulator constructed by the author in a previous paper. We will use this result to deduce some consequences on the kernel and image of the rigid analytic regulator analogous to some old conjectures of Beilinson and Bloch on the complex analytic regulator. We also relate our construction to the symbol deﬁned by Contou-Carrère and to Kato’s residue homomorphism, and we show that Weil’s reciprocity law directly implies the reciprocity law of Anderson and Romo.
Keywords: Regulator, reciprocity laws
Pál Ambrus: On the Kernel and the Image of the Rigid Analytic Regulator in Positive Characteristic. Publ. Res. Inst. Math. Sci. 46 (2010), 255-288. doi: 10.2977/PRIMS/9