# Minimal forms for conics

`2020-12-30 10:30:00``2020-12-30 11:30:00``Minimal forms for conics``A conic is the Severi-Brauer variety of a quaternion algebra Q, and the question of which anisotropic quadratic forms become isotropic over the function field F_Q of a conic has puzzled algebraists for the last three decades. An anisotropic quadratic form is F_Q-minimal if it becomes isotropic over F_Q but any proper subform remains anisotropic. Minimal forms are known to have odd dimension, and examples of minimal forms of any odd dimension were constructed by Hoffmann and Van Geel in characteristic not 2. In this talk, we shall discuss the new analogous examples in characteristic 2 and dimensions 5 and 7. The 7-dimensional example also gives rise to a degree 8 algebra with involution that has $Q$ as a factor as a central simple algebra but not as an algebra with involution. The talk is based on recent joint work with Anne Quéguiner-Mathieu. =========================================== Topic: BIU Algebra Seminar -- Chapman Time: Dec 30, 2020 10:30 AM Jerusalem Meeting ID: 841 3979 5965 Passcode: 795644``Zoom -- see invitation below``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`A conic is the Severi-Brauer variety of a quaternion algebra Q, and the question of which anisotropic quadratic forms become isotropic over the function field F_Q of a conic has puzzled algebraists for the last three decades. An anisotropic quadratic form is F_Q-minimal if it becomes isotropic over F_Q but any proper subform remains anisotropic. Minimal forms are known to have odd dimension, and examples of minimal forms of any odd dimension were constructed by Hoffmann and Van Geel in characteristic not 2. In this talk, we shall discuss the new analogous examples in characteristic 2 and dimensions 5 and 7. The 7-dimensional example also gives rise to a degree 8 algebra with involution that has $Q$ as a factor as a central simple algebra but not as an algebra with involution. The talk is based on recent joint work with Anne Quéguiner-Mathieu.

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Topic: BIU Algebra Seminar -- Chapman

Time: Dec 30, 2020 10:30 AM Jerusalem

Meeting ID: 841 3979 5965

Passcode: 795644

Last Updated Date : 28/12/2020