Curves, Jacobians, and Abelian Varieties

Spring Southeastern Sectional Meeting
University of Virginia, Charlottesville, VA
March 13-15, 2020, Meeting #1143

Organizers:


Dorisa Tabaku Department of Mathematics Oakland University Rochester, MI, 48309. [email protected]	Padmavathi Srinivasan Department of Mathematics Georgia Institute of Technology Atlanta, GA 30313 [email protected]	Tony Shaska Department of Mathematics Oakland University University [email protected]

Overview

Algebraic curves are one of the most classical objects of mathematics, Their study led to the concept of Jacobian and more generally that of an Abelian variety. The goal of this session is to focus on the arithmetic aspects of theory. We will explore minimal models of curves, rational points on curves, Abelian varieties, isogenies, Honda-Tate theory, Weil descent, applications to isogeny based cryptography, etc. The area is a very active area of research and we expect that the session will be well attended. We intend to invite many younger mathematicians, graduate students, and recent PhD’s.

Topics

Equations of curves over their minimal field of definition

Field of moduli versus the field of definition

Models of curves with minimal height

Moduli height of curves

Rational points on curves

Rational points in the moduli space of curves

Jacobians of curves and their decompositions

Neron-Tate models of algebraic curves

Neron-Tate heights on Jacobians

Minimal discriminants and conductors

Selmer groups in Jacobians

Arithmetic invariant theory

Pairings and Weil descent

Mordell-Weil group

Abelian varieties with complex multiplication

Participants