On chow and brauer groups of a product of mumford curves

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Abstract

Let C1, ⋯, Cd be Mumford curves defined over a finite extension of ℚp, and let X = C1 × ⋯ × Cd. We shall show the following: (1) The cycle map CH0(X)/n → H2d (X, μn ⊗d) is injective for any non-zero integer n. (2) The kernel of the canonical map CH0(X) → Hom(Br(X), ℚ/ℤ) (defined by the Brauer-Manin pairing) coincides with the maximal divisible subgroup in CH0(X).

Original languageEnglish
Pages (from-to)549-567
Number of pages19
JournalMathematische Annalen
Volume333
Issue number3
DOIs
Publication statusPublished - 2005 Nov 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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