# Curves, Jacobians, and Abelian Varieties

### Spring Southeastern Sectional Meeting

### University of Virginia, Charlottesville, VA

### March 13-15, 2020

### Meeting #1143

## Special Session: Curves, Jacobians, and Abelian Varieties

### 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 of the session include, but are not limited to:

- 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

**AMS link**

**Speakers**

### Organizers:

**Tony Shaska** (shaska@oakland.edu)

Department of Mathematics and Statistics

Oakland University

Rochester, MI 48386

**Padmavathi Srinivasan** (psrinivasan41@math.gatech.edu)

Department of Mathematics

Georgia Institute of Technology

Atlanta, GA 30313