ICTP Mathematics Seminar - Monday 26 November, at 11:00 - (Davide LOMBARDO)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2018


Monday 26 November, at 11:00 hrs.


Davide Lombardo (University of Pisa)

Title: Endomorphism rings of Jacobians


Abstract:

Over the last two centuries mathematicians have developed a very rich 
theory of abelian varieties; however, certain kinds of explicit 
calculations have remained out of reach of our computational power until 
quite recently, when theoretical and technological advances have led to 
a renewed interest in the computational side of the theory. In this talk 
I will discuss one of the fundamental algorithmic problems one would 
like to solve, namely that of determining the endomorphism ring of the 
Jacobian of an explicitly given curve over a number field. I will 
describe a method to compute the endomorphism ring of such a Jacobian, 
starting with the case of genus-2 curves, and show the connection 
between this problem and a certain local-global principle for the center 
of the endomorphism algebra. If time permits, I will also outline how to 
prove the necessary local-global principle for abelian surfaces and, 
under the assumption of the Mumford-Tate conjecture, for all abelian 
varieties.


VENUE: 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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