The Structure of Groups Attached to Algebraic Varieties
When
4 – 5 p.m., Oct. 22, 2026
Where
Math, Room 501
Title: The Structure of Groups Attached to Algebraic Varieties
Abstract: Let K be an infinite field such as the complex numbers, for example. The structure of many well-known groups that are attached to an algebraic variety over K depend on the size of K. For example, the group of K-points of an algebraic group over K has the same cardinality as that of K, so will be countable or uncountable as K is. Other groups, such as singular cohomology with integral coefficients of the underlying topological space of an algebraic variety over the complex numbers, are finitely generated. In this talk, I will discuss some objects such as certain motivic cohomology groups of algebraic varieties, whose group structure is expected to be sort of in between. These are expected to be countable groups even as the field K may be uncountable. This is sometimes called “rigidity.” All terms used here will be defined in the talk.