Diophantine problems over tamely ramified fields

DOI10.1016/J.JALGEBRA.2022.10.022arXiv2103.14646MaRDI QIDQ6363853

Publication date: 26 March 2021

Abstract: Assuming a certain form of resolution of singularities, we prove a general existential Ax-Kochen/Ershov principle for tamely ramified fields in all characteristics. This specializes to well-known results in residue characteristic

0

and unramified mixed characteristic. It also encompasses the conditional existential decidability results known for

m a t h b b F_{p} (! (t)!)

and its finite extensions, due to Denef-Schoutens. On the other hand, it also applies to the setting of infinite ramification, providing us with an abundance of infinitely ramified extensions of

m a t h b b Q_{p}

and

m a t h b b F_{p} (! (t)!)

that are existentially decidable.

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Model-theoretic algebra (03C60)

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