On chow and brauer groups of a product of mumford curves

Takao Yamazaki

doi:10.1007/s00208-005-0675-x

On chow and brauer groups of a product of mumford curves

Takao Yamazaki

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

Let C₁, ⋯, C_d be Mumford curves defined over a finite extension of ℚ_p, and let X = C₁ × ⋯ × C_d. We shall show the following: (1) The cycle map CH₀(X)/n → H_2d (X, μ_n ^⊗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 language	English
Pages (from-to)	549-567
Number of pages	19
Journal	Mathematische Annalen
Volume	333
Issue number	3
DOIs	https://doi.org/10.1007/s00208-005-0675-x
Publication status	Published - 2005 Nov 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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AB - 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).

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On chow and brauer groups of a product of mumford curves

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