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.
You are here
Endomorphism rings of Jacobians
Speaker:
Davide Lombardo
Institution:
University of Pisa
Schedule:
Monday, November 26, 2018 - 11:00
Location:
Luigi Stasi Seminar Room, ICTP
Abstract:
Openings
- Call of interest for positions in mathematics at SISSA
- Public Calls for Professors
- Temporary Researchers
- Post Doctoral Fellowships
- Open positions in MathLab
- SISSA Mathematical Fellowships
- PhD Scolarships
- SIS Fellowships
- Pre-PhD Fellowships
- MSc in Mathematics
- Master Degree in Data Science and Scientific Computing
- Professional Master Courses
- SISSA Mathematics Medals
Upcoming events
-
Antonio De Rosa
Min-max construction of anisotropic CMC surfaces
Thursday, May 16, 2024 - 14:00 to 16:00
-
Mattia Fogagnolo
The isoperimetric mass in nonnegative scalar curvature beyond smoothness and asymptotic flatness
Thursday, May 30, 2024 - 14:00 to 16:00
-
Marco Pozzetta
TBA
Thursday, June 13, 2024 - 14:00 to 15:00
Today's Lectures
-
11:00 to 13:00
-
14:00 to 16:00
Recent publications
-
G.P. Leonardi; G. Saracco,Rigidity and trace properties...
-
R. Marchello; A. Colombi; L. Preziosi; C. Giverso,A non local model for cell mig...
-
I. Prusak; D. Torlo; M. Nonino; G. Rozza,Optimisation–Based Coupling of...
-
A.Surya Boiardi; R. Marchello,Breaking the left-right symmet...