Formal group law of an algebraic group

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Definition

Suppose G is an algebraic group over a field k. The formal group law of G is a formal group law over k obtained by taking coordinates in an affine neighborhood of the identity, setting the identity element as the origin for the coordinates.

Facts

  • The formal group law of an algebraic group is the same as the formal group law of its connected component of identity. In particular, the formal group law depends only on the connected component of identity.