As in the last ehapter we begin with matrices and then generalize to a class of group schemes; the matrices involved here are at the other extreme from separability. What we want is some version of nilpotence, but of course nilpotent matrices cannot occur in a group, so we modify the definition slightly. Call an element g inGL n (k) unipotent if g − 1 is nilpotent— equivalently, all eigenvalues of g should be 1.
Unable to display preview. Download preview PDF.