Establishes first-order definability of Campana and Darmon points in algebraic function fields over number fields by extending quadratic Pfister form methods from prior number field results.
Universally defining subrings in function fields
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We establish that all rings of $S$-integers are universally definable in function fields in one variable over certain ground fields including global and non-archimedean local fields. That is, we show that the complement of such a ring of $S$-integers is always a diophantine set. As a technical tool, we use a reciprocity exact sequence for quadratic Witt groups in function fields over almost arbitrary base fields (of any characteristic), which is new and of potentially independent interest.
fields
math.NT 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
First-order definability of Campana Points and Darmon Points in algebraic function fields in one variable over number fields
Establishes first-order definability of Campana and Darmon points in algebraic function fields over number fields by extending quadratic Pfister form methods from prior number field results.