A note on quadratic forms

Fabian Hebestreit; Achim Krause; Maxime Ramzi

doi:10.1112/blms.13028

A note on quadratic forms

Fabian Hebestreit^*, Achim Krause, Maxime Ramzi

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

For a field extension (Formula presented.) we consider maps that are quadratic over (Formula presented.) but whose polarisation is only bilinear over (Formula presented.). Our main result is that all such are automatically quadratic forms over (Formula presented.) in the usual sense if and only if (Formula presented.) is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic forms is superfluous.

Original language	English
Journal	Bulletin of the London Mathematical Society
Volume	56
Issue number	5
Pages (from-to)	1803-1818
ISSN	0024-6093
DOIs	https://doi.org/10.1112/blms.13028
Publication status	Published - 2024

Bibliographical note

Publisher Copyright:
© 2024 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.

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Cite this

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AU - Hebestreit, Fabian

AU - Krause, Achim

AU - Ramzi, Maxime

PY - 2024

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N2 - For a field extension (Formula presented.) we consider maps that are quadratic over (Formula presented.) but whose polarisation is only bilinear over (Formula presented.). Our main result is that all such are automatically quadratic forms over (Formula presented.) in the usual sense if and only if (Formula presented.) is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic forms is superfluous.

AB - For a field extension (Formula presented.) we consider maps that are quadratic over (Formula presented.) but whose polarisation is only bilinear over (Formula presented.). Our main result is that all such are automatically quadratic forms over (Formula presented.) in the usual sense if and only if (Formula presented.) is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic forms is superfluous.

U2 - 10.1112/blms.13028

DO - 10.1112/blms.13028

M3 - Journal article

AN - SCOPUS:85189795773

VL - 56

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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