GEISSER, Thomas; MORIN, Baptiste

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GEISSER, Thomas

MORIN, Baptiste
Institut de Mathématiques de Bordeaux [IMB]

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Let K be a finite extension of the p-adic numbers Qp with ring of integers OK , X a regular scheme, proper, flat, and geometrically irreducible over OK of dimension d, and XK its generic fiber. We show, under some assumptions on XK , that there is a reciprocity isomorphism of locally compact groups H 2d−1 ar (XK , Z(d)) ≃ π ab 1 (XK)W from the cohomology theory defined in [9] to an integral model π ab 1 (XK)W of the abelianized geometric fundamental groups π ab 1 (XK) geo. After removing the contribution from the base field, the map becomes an isomorphism of finitely generated abelian groups. The key ingredient is the duality result in [9].< Réduire

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1991 Mathematics Subject Classification. Primary: 14G45

Secondary: 11G25

14G20

14F42

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ON INTEGRAL CLASS FIELD THEORY FOR VARIETIES OVER p-ADIC FIELDS

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Résumé en anglais

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