##  [Cycle Class Map](/cycle-class-map) 

  ##  [Cycle Class Map](https://algebra.quantumdictionary.io/cycle-class-map-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A natural homomorphism from groups of algebraic cycles (e.g., Chow groups CH^p(X)) to a chosen cohomology theory (singular, De Rham, étale, Deligne, etc.), which sends an algebraic subvariety to its cohomology class (for example CH^p(X) → H^{2p}(X, Z(p))).