Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields

Kirsten Eisenträger

doi:10.1016/j.jalgebra.2006.09.032

Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields

Kirsten Eisenträger

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n ≥ 1 over k. Then Hilbert's Tenth Problem for L is undecidable. In particular, Hilbert's Tenth Problem for function fields of varieties over number fields of dimension ≥1 is undecidable.

Original language	English (US)
Pages (from-to)	775-792
Number of pages	18
Journal	Journal of Algebra
Volume	310
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2006.09.032
State	Published - Apr 15 2007

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2006.09.032

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title = "Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields",

abstract = "Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n ≥ 1 over k. Then Hilbert's Tenth Problem for L is undecidable. In particular, Hilbert's Tenth Problem for function fields of varieties over number fields of dimension ≥1 is undecidable.",

author = "Kirsten Eisentr{\"a}ger",

note = "Funding Information: I thank Brian Conrad and Thanases Pheidas for several helpful discussions. I also thank Laurent Moret-Bailly for suggesting a way to simplify the proof of Theorem 5.4. Most of the research was done while the author was partially supported by the National Science Foundation under agreement No. DMS-0111298.",

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N1 - Funding Information: I thank Brian Conrad and Thanases Pheidas for several helpful discussions. I also thank Laurent Moret-Bailly for suggesting a way to simplify the proof of Theorem 5.4. Most of the research was done while the author was partially supported by the National Science Foundation under agreement No. DMS-0111298.

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N2 - Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n ≥ 1 over k. Then Hilbert's Tenth Problem for L is undecidable. In particular, Hilbert's Tenth Problem for function fields of varieties over number fields of dimension ≥1 is undecidable.

AB - Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n ≥ 1 over k. Then Hilbert's Tenth Problem for L is undecidable. In particular, Hilbert's Tenth Problem for function fields of varieties over number fields of dimension ≥1 is undecidable.

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Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields

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