For a proper smooth variety X defined over a local field k, unramified class field theory investigates the reciprocity map øX : SK1 (X) → πab1 (X) as introduced by S. Saito. We study this map in the case when X is a surface admitting a proper surjection onto a smooth geometrically connected curve C with a smooth conic as generic fibre. Without any assumption on the reduction of C, we prove that øX is injective modulo n for all n invertible in k and its cokernel is the same as that of øC. © 1999 Kluwer Academic Publishers.
Sur l'application de réciprocité pour une surface fibrée en coniques définie sur un corps local
Szamuely, Tamás
Primo
1999-01-01
Abstract
For a proper smooth variety X defined over a local field k, unramified class field theory investigates the reciprocity map øX : SK1 (X) → πab1 (X) as introduced by S. Saito. We study this map in the case when X is a surface admitting a proper surjection onto a smooth geometrically connected curve C with a smooth conic as generic fibre. Without any assumption on the reduction of C, we prove that øX is injective modulo n for all n invertible in k and its cokernel is the same as that of øC. © 1999 Kluwer Academic Publishers.File in questo prodotto:
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