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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Discrete valuation rings
- Linear algebraic groups and torsors
- Local-global principles
- Semiglobal fields