Prudent group schemes over a complete discrete valuation ring


Venue/Location: C2-714, VIASM

Speaker: Prof. Phùng Hồ Hải

An affine group scheme is completely determined by its coordinate ring, which is a (commutative Hopf algebra). Among flat affine group schemes over a Dedekind ring, those which have coordinate rings projective (over the base ring) have many good properties. We are looking for conditions for an affine group scheme over a Dedekind ring, or more specific, over a discrete valuation ring, to have projective coordinate ring. When the base ring is a complete discrete valuation ring, this property is equivalent to being prudent, a property that can be checked on each finite quotient of the base ring. We show various applications of this property.
This is a joint work with J.P.P. dos Santos (Paris).