Difference between revisions of "NTS ABSTRACTSpring2017"

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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]
== Jan 25 ==
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''David Zureick-Brown'''
| bgcolor="#BCD2EE"  align="center" | Progress on Mazur’s program B
| bgcolor="#BCD2EE"  | I’ll discuss recent progress on Mazur’s ”Program B”, including my own recent work with Jeremy Rouse which completely classifies the possibilities for the 2-adic image of Galois associated to an elliptic curve over the rationals. I will also discuss a large number of other very recent results by many authors.

Revision as of 16:15, 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.