I've been doing some reading in some arithmetic geometry, and there's a subtle point that is confusing me slightly: say $U$ is some unipotent affine group scheme over a field $L$, and $T$ is some right $U$-torsor. Then the claim is that $T$ contains a global point over $L$ i.e. $T(L) \neq \emptyset$.
I'm really not that sure on where to go with this, and how to demonstrate existence of these global points? Any help would be appreciated!