Difference between revisions of "NTS ABSTRACTSpring2017"
Jump to navigation
Jump to search
Line 1: | Line 1: | ||
Return to [https://www.math.wisc.edu/wiki/index.php/NTS NTS Spring 2017] | Return to [https://www.math.wisc.edu/wiki/index.php/NTS NTS Spring 2017] | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
Revision as of 17:15, 18 December 2017
Return to NTS Spring 2017
Feb 1
Yunqing Tang |
Exceptional splitting of reductions of abelian surfaces with real multiplication |
Abstract: Zywina showed that after passing to a suitable field extension, every abelian surface $A$ with real multiplication over some number field has geometrically simple reduction modulo $\frak{p}$ for a density one set of primes $\frak{p}$. One may ask whether its complement, the density zero set of primes $\frak{p}$ such that the reduction of $A$ modulo $\frak{p}$ is not geometrically simple, is infinite. Such question is analogous to the study of exceptional mod $\frak{p}$ isogeny between two elliptic curves in the recent work of Charles. In this talk, I will show that abelian surfaces over number fields with real multiplication have infinitely many non-geometrically-simple reductions. This is joint work with Ananth Shankar. |