Abelian Varieties Multi-Site Seminar Series: Drew Sutherland
Topic
Sato-Tate Distributions of Abelian Varieties [video]
Speakers
Details
Let A be an abelian variety of dimension g over a number field K. The Sato-Tate group ST(A) is a compact subgroup of the unitary symplectic group USp(2g) that can be defined in terms of the l-adic Galois representation associated to A. Under the generalized Sato-Tate conjecture, the Haar measure of ST(A) governs the distribution of various arithmetic statistics associated to A, including the distribution of normalized Frobenius traces at primes of good reduction.
The Sato-Tate groups that can and do arise for g=1 and g=2 have been completely determined, but the case g=3 remains open. I will give a brief overview of the classification for g=2 and then discuss the current state of progress for g=3.
The Sato-Tate groups that can and do arise for g=1 and g=2 have been completely determined, but the case g=3 remains open. I will give a brief overview of the classification for g=2 and then discuss the current state of progress for g=3.
Additional Information
A [video] of this event is available on mathtube.org.
Bluejeans connection info:
Meeting Title: AV-CRG-Seminars 2016 - Tuesday 1.12.16 Session
Meeting Time: Tuesday January 12, 2016 • noon MST / 1 hr
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Drew Sutherland, Massachusetts Institute of Technology