# On the cohomologies of commutative affine group schemes

@inproceedings{Miyanishi1968OnTC, title={On the cohomologies of commutative affine group schemes}, author={Masayoshi Miyanishi}, year={1968} }

- Published 1968
DOI:10.1215/kjm/1250524175

Let k be an algebraically closed field of positive characteristic p, x a proper integral k-scheme o f finite type and G b e a commutative affine k-group scheme. For a k-prescheme T , the isomorphism classes o f principal fibre spaces Y over X T with group G form an abelian group with the well-known multiplication. We shall denote this abelian group by PH(G, X / k ) ( T ) . Then the functor X / k)(T ) is a contravariant functor from the category o f k-preschemes (Sch/k) to the category o f… CONTINUE READING