Galois cohomology

Galois cohomology is a branch of mathematics that studies how symmetries of algebraic structures, like field extensions, influence their properties. It uses tools from cohomology, a method for measuring the ways objects can be twisted or fail to be compatible under these symmetries, to understand solutions to equations and classify algebraic structures. Essentially, it helps mathematicians analyze how certain algebraic systems behave under transformations, revealing deep connections between field theory, group actions, and algebraic geometry.