Let $K$ be a finite Galois extension of a field $k$. Let $X$ be a variety defined over $k.$ In a paper I am reading, it mentions splitting of 1 -cocycles. For example, "a 1-cocycle $c \in Z^1(\Gamma(K/k),X)$ splits." What does this mean?
2026-03-27 14:21:46.1774621306
What does it mean for a 1-cocycle to split?
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I found the answer in Lang's paper "On Quasi-Algebraic Closure." I think it just means that it is a coboundary.