A note on quadratic forms
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A note on quadratic forms. / Hebestreit, Fabian; Krause, Achim; Ramzi, Maxime.
In: Bulletin of the London Mathematical Society, 2024.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - A note on quadratic forms
AU - Hebestreit, Fabian
AU - Krause, Achim
AU - Ramzi, Maxime
N1 - Publisher Copyright: © 2024 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2024
Y1 - 2024
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
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
ER -
ID: 389924564