Groups of Russell type over a curve Original Research Article

We consider groups of Russell type over a curve, which are forms of Ga-bundle over a curve. In this article, we show that groups of Russell type over a curve, not necessarily a Tango curve, are associated with locally free sheaves of rank two on the base curve. Moreover, these locally free sheaves are often stable but their Frobenius pull-backs are not stable. We observe also pathological phenomena on completions of groups of Russell type, namely, the existence of non-closed global differential forms and the non-reducedness of the automorphism group scheme.