BCN Spring 2016 Workshop: Number Theory & K-theory

Motivic homology and spaces of algebraic cycles.


Abdó Roig-Maranges


In this talk I'll describe some ideas of Friedlander and Lawson, to producemotivic invariants of a complex algebraic variety $X$ using the topology of the moduli space of its algebraic cycles. In particular, I'll explain how toconstruct a version of motivic homology modulo algebraic equivalence.

Then, I'll discuss the construction of intersection products on those invariants, and present some recent results using them to prove a blow-up formula for regularly embedded varieties.

Finally, I'll discuss some open problems and future directions with a particular emphasis on how to extend the definition of these semi-topological kind of invariants to other fields.


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