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DTSTAMP:20170910T170506Z
DTSTART;TZID=America/Los_Angeles:20170911T151000
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SUMMARY:Arithmetic Geometry and Number Theory RTG Seminar: Exceptional splitting of reductions of abelian surfaces with real multiplication
UID:111464-ucb-events-calendar@berkeley.edu
ORGANIZER;CN="UC Berkeley Calendar Network":
LOCATION:891 Evans Hall
DESCRIPTION:Yunqing Tang\, Princeton University\n\nZywina 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 $\\mathfrak p$ for a density one set of primes $\\mathfrak p$. One may ask whether its complement\, the density zero set of primes $\\mathfrak p$ such that the reduction of $A$ modulo $\\mathfrak p$ is not geometrically simple\, is infinite. Such question is analogous to the study of exceptional mod $\\mathfrak p$ 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.\n\nSeminar Format: The seminar consists of two 50-minute talks\, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00)\, with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory\; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.
URL:http://events.berkeley.edu/index.php/calendar/sn/pubaff.html?event_ID=111464&view=preview
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