ICTP Mathematics Seminar - Monday, 27 May, at 14:30 (Victoria Cantora-Farfán)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2019


Monday 27 May, at 14:30 hrs.


Victoria Cantoral-Farfán (ICTP)


Title: On an algebraic Sato–Tate conjecture for abelian varieties


Abstract: The Sato-Tate conjecture, originally stated for elliptic 
curves without complex multiplication, predicts the equidistribution of 
the normalized Frobenius traces with respect to the Sato-Tate measure, 
given by the pushforward of the Haar measure on SU(2). We would like to 
work on an analogous question for abelian varieties of dimension /g >/ 
1; the generalized Sato-Tate conjecture, introduced by Serre, which 
predicts the equidistribution on a certain compact Lie group: the 
Sato-Tate group. In 1966, Serre presented remarkable links between the 
Mumford-Tate group and the Sato-Tate group. Thus, the algebraic 
Sato-Tate group appears as an intermediate group between the 
Mumford-Tate group and the Sato-Tate group. Indeed, if the algebraic 
Sato-Tate conjecture holds for some particular abelian variety A of 
dimension /g >/ 1, we can obtain the Sato-Tate group and try to deduce 
some new instances of the generalized Sato-Tate conjecture. The main 
goal of this talk is to present new results in the direction of the 
algebraic Sato-Tate conjecture, building on the previous work of Serre, 
Kedlaya and Banaszak.


http://indico.ictp.it/event/8941/


VENUE: Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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