Witt Vector - Commutative Unipotent Algebraic Groups

Commutative Unipotent Algebraic Groups

Over an algebraically closed field of characteristic 0, any unipotent abelian connected algebraic group is isomorphic to a product of copies of the additive group Ga. The analogue of this for fields of characteristic p is false: the truncated Witt schemes are counterexamples. (We make them into algebraic groups by forgetting the multiplication and just using the additive structure.) However these are essentially the only counterexamples: over an algebraically closed field of characteristic p, any unipotent abelian connected algebraic group is isogenous to a product of truncated Witt group schemes.

Read more about this topic:  Witt Vector

Famous quotes containing the words algebraic and/or groups:

    “I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
    —Henry David Thoreau (1817–1862)

    “The awareness of the all-surpassing importance of social groups is now general property in America.”
    —Johan Huizinga (1872–1945)