Amitsur Algebra Seminar
Time: Thursday, January 6, at 12:00.
Place: room 209, Mathematics building
Speaker: Darrell Eugene Haile
Title: The Clifford algebra of a quartic curve of genus one
This is joint work with Ilseop Han. For each irreducible quartic f over a
field k, we construct a k-algebra A_f associated to the hyperelliptic affine
curve C:y^2=f(x). We prove that A_f has many interesting properties. For
example it is an Azumaya algebra of rank 4 over its center and its center is
the coordinate ring of the affine elliptic curve E related to the Jacobian
of C. Each simple image of A_f is a quaternion algebra. The simple images
with center k then come from the rational points on E and the resulting
function from the group of rational points on E to the Brauer group of k is
a group homomorphism. We also prove that A_f is split if and only if the
curve C has a k-rational point.
You are cordially invited!
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel <firstname.lastname@example.org>
Announcement from: Gili Schul <email@example.com>