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Diagonal Forms of Higher Degree Over Function Fields of p-adic Curves

Pumpl�n, S.; Pumpluen, S.

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Authors

S. Pumpl�n



Abstract

We investigate diagonal forms of degree d over the function field F of a smooth projective p-adic curve: if a form is isotropic over the completion of F with respect to each discrete valuation of F , then it is isotropic over certain fields F_U , F_P and F_p. These fields appear naturally when applying the methodology of patching; F is the inverse limit of the finite inverse system of fields {F_U , F_P , F_p}. Our observations complement some known bounds on the higher u-invariant of diagonal forms of degree d. We only consider diagonal forms of degree d over fields of characteristic not dividing d!.

Journal Article Type Article
Acceptance Date Jul 1, 2019
Online Publication Date Sep 5, 2019
Publication Date Feb 1, 2020
Deposit Date Sep 11, 2019
Publicly Available Date Sep 6, 2020
Journal International Journal of Number Theory
Print ISSN 1793-0421
Electronic ISSN 1793-7310
Publisher World Scientific
Peer Reviewed Peer Reviewed
Volume 16
Issue 1
Pages 161-172
DOI https://doi.org/10.1142/S1793042120500098
Keywords Forms of higher degree; Diagonal forms; Function fields; p-adic curves; u- invariant mathematics
Public URL https://nottingham-repository.worktribe.com/output/2248895
Publisher URL https://www.worldscientific.com/doi/abs/10.1142/S1793042120500098?journalCode=ijnt
Additional Information Electronic version of an article published as Diagonal forms of higher degree over function fields of p-adic curves
S. Pumplün (School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK)
International Journal of Number Theory 2020 16:01, 161-172 https://doi.org/10.1142/S1793042120500098 © World Scientific Publishing Company] https://www.worldscientific.com/worldscinet/ijnt

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