Non-vanishing of Ceresa and Gross--Kudla--Schoen cycles

Series
Number Theory
Time
Wednesday, April 9, 2025 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Wanlin Li – Washington University – wanlin@wustl.eduhttps://www.math.wustl.edu/~wanlin/
Organizer
Joshua Stucky

The Ceresa cycle and the Gross—Kudla—Schoen modified diagonal cycle are algebraic $1$-cycles associated to a smooth algebraic curve. They are algebraically trivial for a hyperelliptic curve and non-trivial for a very general complex curve of genus $>2$. Given an algebraic curve, it is an interesting question to study whether the Ceresa and GKS cycles associated to it are rationally or algebraically trivial. In this talk, I will discuss some methods and tools to study this problem