##  [Cohomological Dimension](/cohomological-dimension) 

  ##  [Cohomological Dimension](https://mathlogic.quantumdictionary.io/cohomological-dimension-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The largest integer n (or infinity) such that a given group or topological space has nontrivial cohomology in degree n with coefficients in some module (or system of coefficients); for groups this is often the supremum of degrees in which group cohomology with appropriate modules is nonzero.

 

 

 

 

 





 

 



 ##  [Cohomological Dimension](https://algebra.quantumdictionary.io/cohomological-dimension-1) 

  

 [![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

The largest integer n (or infinity) such that cohomology with specified coefficients can be nonzero; applied to spaces, groups, or schemes, it measures the topological or algebraic complexity detectable by cohomology.