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

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)5263-5286
Number of pages24
JournalTransactions of the American Mathematical Society
Volume372
Issue number8
DOIs
StatePublished - Oct 15 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Discrete valuation rings
  • Linear algebraic groups and torsors
  • Local-global principles
  • Semiglobal fields
  • Zero-cycles

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