In mathematics, geometric class field theory is an extension of class field theory to higher-dimensional geometrical objects: much the same way as class field theory describes the abelianization of the Galois group of a local or global field, geometric class field theory describes the abelianized fundamental group of higher dimensional schemes in terms of data related to algebraic cycles.

References

• Schmidt, Alexander (2015). "A survey on class field theory for varieties". In Ballet, Stéphane; Perret, Marc; Zaytsev, Alexey (eds.). Algorithmic arithmetic, geometry, and coding theory. Amer. Math. Soc. pp. 301–306. ISBN 978-1-4704-1461-0.