# From elliptic curves to Ceresa cycles

Speaker
Ari Shnidman (Hebrew University)
Date
10/03/2024 - 13:00 - 12:00Add to Calendar 2024-03-10 12:00:00 2024-03-10 13:00:00 From elliptic curves to Ceresa cycles Given an algebraic variety X, and two subvarieties Y, Y', can Y be deformed to Y' within X?  More generally, we would like to understand the different "deformation classes" of subvarieties of X of a given dimension.  For topological deformations, the answer is given by singular cohomology and is rather well understood.  For algebraic deformations, the answer is quite mysterious and depends heavily on the ground field. In codimension 1, this amounts to studying rational points on abelian varieties (such as elliptic curves). In higher codimension, much less is understood.  I'll survey this topic and conclude by giving some new results in codimension two, concerning the so-called Ceresa cycles. hybrid mode: math building (216), room 201, and zoom: https://biu-ac-il.zoom.us/j/751076379 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
hybrid mode: math building (216), room 201, and zoom: https://biu-ac-il.zoom.us/j/751076379
Abstract

Given an algebraic variety X, and two subvarieties Y, Y', can Y be deformed to Y' within X?

More generally, we would like to understand the different "deformation classes" of subvarieties of X of a given dimension.  For topological deformations, the answer is given by singular cohomology and is rather well understood.  For algebraic deformations, the answer is quite mysterious and depends heavily on the ground field. In codimension 1, this amounts to studying rational points on abelian varieties (such as elliptic curves). In higher codimension, much less is understood.

I'll survey this topic and conclude by giving some new results in codimension two, concerning the so-called Ceresa cycles.

תאריך עדכון אחרון : 10/03/2024