skip to main content
Caltech
Fires burning in Greater Los Angeles area have had significant impact on the Caltech's community and surrounding areas. For information and resources for members of the Caltech community, go to https://www.caltech.edu/fire.

Number Theory Seminar

Thursday, May 17, 2018
4:00pm to 5:00pm
Add to Cal
Building 15, Room 104
A split-complex analogue of abelian varieties
Zavosh Amir-Khosravi, Department of Mathematics, Caltech,
The split-complex numbers are the split quadratic extension of the reals. We define the analogue of a complex abelian variety over this ring as a polarized split-complex torus, and show that a number of classical results about abelian varieties have split-complex analogues. For instance, principally polarized split-complex tori are parametrized by an arithmetic quotient of the symmetric space of $O(n,n)$, and there is a natural notion of real multiplication, corresponding to special points on the moduli space. We describe a construction relating these objects to abelian varieties, and discuss reciprocity laws, $p$-divisible groups, and a connection with abelian varieties over R.
For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at mathinfo@caltech.edu.