##  [Étale Cohomology](/etale-cohomology) 

  ##  [Étale Cohomology](https://puremath.quantumdictionary.io/etale-cohomology-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sheaf cohomology theory on the étale site of a scheme that assigns cohomological invariants to schemes and varieties, bridging algebraic geometry, arithmetic and analogues of topological cohomology (e.g., l-adic cohomology and comparison theorems).

 

 

 

 

 





 

 



 ##  [Étale Cohomology](https://algebra.quantumdictionary.io/etale-cohomology-1) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sheaf cohomology theory computed on the étale site of a scheme, producing groups H^i_et(X, F) for étale sheaves F (and their l-adic completions) that reflect arithmetic and geometric information, and carry Galois actions for varieties over non algebraically closed fields.