Difference between revisions of "NTS ABSTRACTSpring2018"
From UW-Math Wiki
(Created page with "Return to [https://www.math.wisc.edu/wiki/index.php/NTS NTS Spring 2018] == Feb 1 == <center> {| style="color:black; font-size:100%" table border="2" cellpadding="10" wid...") |
|||
Line 1: | Line 1: | ||
− | Return to [https://www.math.wisc.edu/wiki/index.php/ | + | Return to [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_2018] |
Revision as of 17:17, 18 December 2017
Return to [1]
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. |