@article{fedffc7841f347ef9afb8b59f1eb2482,
title = "Local-global principles for zero-cycles on homogeneous spaces over arithmetic function fields",
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.",
keywords = "Discrete valuation rings, Linear algebraic groups and torsors, Local-global principles, Semiglobal fields, Zero-cycles",
author = "Colliot-Th{\'e}l{\`e}ne, {J. L.} and D. Harbater and J. Hartmann and D. Krashen and R. Parimala and V. Suresh",
note = "Funding Information: Received by the editors April 15, 2018. 2010 Mathematics Subject Classification. Primary 14C25, 14G05, 14H25; Secondary 11E72, 12G05, 12F10. Key words and phrases. Linear algebraic groups and torsors, zero-cycles, local-global principles, semiglobal fields, discrete valuation rings. The second and third authors were supported by NSF collaborative FRG grant DMS-1463733. The second author was also supported by NSF collaborative FRG grant DMS-1265290, and the third author by a Simons Fellowship. The fourth author was supported by NSF collaborative FRG grant DMS-1463901. This author was also supported by NSF RTG grant DMS-1344994. The fifth and sixth authors were supported by NSF collaborative FRG grant DMS-1463882. The fifth author was also supported by NSF grant DMS-1401319, and the sixth author by NSF grant DMS-1301785. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society",
year = "2019",
month = oct,
day = "15",
doi = "10.1090/tran/7911",
language = "English (US)",
volume = "372",
pages = "5263--5286",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "8",
}