# Minimal forms for conics

Seminar
Speaker
Date
30/12/2020 - 11:30 - 10:30Add to Calendar 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 - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Zoom -- see invitation below
Abstract

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

תאריך עדכון אחרון : 28/12/2020