Local-global principles for zero-cycles on homogeneous spaces over arithmetic function fields

Colliot-Thélène, J.-L.; Harbater, D.; Hartmann, J.; Krashen, D.; Parimala, R.; Suresh, V.

doi:10.1090/tran/7911

Local-global principles for zero-cycles on homogeneous spaces over arithmetic function fields
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by J.-L. Colliot-Thélène, D. Harbater, J. Hartmann, D. Krashen, R. Parimala and V. Suresh PDF

Trans. Amer. Math. Soc. 372 (2019), 5263-5286 Request permission

Abstract:

We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. We show that local-global principles hold for such zero-cycles provided that local-global principles hold for the existence of rational points over extensions of the function field. This assertion is analogous to a known result concerning varieties over number fields. Many of our results are shown to hold more generally in the henselian case.

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