Abstract
Quadratic descent of generalized quadratic forms over a division algebra with involution of the first kind in characteristic two is investigated. Using the notion of transfer, it is shown that a system of quadratic forms, associated to such a generalized quadratic form, can be used to characterize its descent properties.
Keywords
Generalized quadratic form system of quadratic forms division algebra with involution quadratic extension quadratic descent
References
- E. Bayer-Fluckiger and H. W. Lenstra, Jr., Forms in odd degree extensions and self-dual normal bases, Amer. J. Math., 112(3) (1990), 359-373.
- R. Elman, N. Karpenko and A. Merkurjev, The Algebraic and Geometric Theory of Quadratic Forms, American Mathematical Society Colloquium Publications, 56, American Mathematical Society, Providence, RI, 2008.
- M. A. Elomary and J.-P. Tignol, Classification of quadratic forms over skew fields of characteristic 2, J. Algebra, 240(1) (2001), 366-392.
- M.-A. Knus, Quadratic and Hermitian Forms Over Rings, Grundlehren der Mathematischen Wissenschaften, 294, Springer-Verlag, Berlin, 1991.
- M.-A. Knus, A. Merkurjev, M. Rost and J.-P. Tignol, The Book of Involutions, American Mathematical Society Colloquium Publications, 44, American Mathematical Society, Providence, RI, 1998.
- A. H. Nokhodkar, Hermitian forms and systems of quadratic forms, Doc. Mat., 23 (2018), 747-758.
- A. H. Nokhodkar, Quadratic descent of hermitian forms, Math. Nachr., 292(10) (2019), 2294-2299.
- A. H. Nokhodkar, Erratum to the paper “Quadratic descent of hermitian forms”, Math. Nachr., 293(9) (2020), 1836-1838.
- A. H. Nokhodkar, Applications of systems of quadratic forms to generalised quadratic forms, Bull. Aust. Math. Soc., 102(3) (2020), 374-386.
- A. Pfister, Quadratic forms with Applications to Algebraic Geometry and Topology, London Mathematical Society Lecture Note Series, 217, Cambridge University Press, Cambridge, 1995.
- J. Tits, Formes quadratiques, groupes orthogonaux et algebres de Clifford, Invent. Math., 5 (1968), 19-41.
Abstract
References
- E. Bayer-Fluckiger and H. W. Lenstra, Jr., Forms in odd degree extensions and self-dual normal bases, Amer. J. Math., 112(3) (1990), 359-373.
- R. Elman, N. Karpenko and A. Merkurjev, The Algebraic and Geometric Theory of Quadratic Forms, American Mathematical Society Colloquium Publications, 56, American Mathematical Society, Providence, RI, 2008.
- M. A. Elomary and J.-P. Tignol, Classification of quadratic forms over skew fields of characteristic 2, J. Algebra, 240(1) (2001), 366-392.
- M.-A. Knus, Quadratic and Hermitian Forms Over Rings, Grundlehren der Mathematischen Wissenschaften, 294, Springer-Verlag, Berlin, 1991.
- M.-A. Knus, A. Merkurjev, M. Rost and J.-P. Tignol, The Book of Involutions, American Mathematical Society Colloquium Publications, 44, American Mathematical Society, Providence, RI, 1998.
- A. H. Nokhodkar, Hermitian forms and systems of quadratic forms, Doc. Mat., 23 (2018), 747-758.
- A. H. Nokhodkar, Quadratic descent of hermitian forms, Math. Nachr., 292(10) (2019), 2294-2299.
- A. H. Nokhodkar, Erratum to the paper “Quadratic descent of hermitian forms”, Math. Nachr., 293(9) (2020), 1836-1838.
- A. H. Nokhodkar, Applications of systems of quadratic forms to generalised quadratic forms, Bull. Aust. Math. Soc., 102(3) (2020), 374-386.
- A. Pfister, Quadratic forms with Applications to Algebraic Geometry and Topology, London Mathematical Society Lecture Note Series, 217, Cambridge University Press, Cambridge, 1995.
- J. Tits, Formes quadratiques, groupes orthogonaux et algebres de Clifford, Invent. Math., 5 (1968), 19-41.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Research Article |
| Authors | |
| Submission Date | November 13, 2023 |
| Acceptance Date | April 29, 2024 |
| Early Pub Date | May 8, 2024 |
| Publication Date | January 14, 2025 |
| DOI | https://doi.org/10.24330/ieja.1480447 |
| IZ | https://izlik.org/JA22XM28FE |
| Published in Issue | Year 2025 Volume: 37 Issue: 37 |