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Group algebras of the additive group. (Algèbres de groupe du groupe additif.) (French) Zbl 0735.13013
Summary: Let \(k\) be a perfect field of positive characteristic, let \(\alpha\) be the additive group and let \(W\) be the Witt vector ring. We compute the group algebra and the group \(W\)-algebra of \(\alpha\) in the sense of affine schemes. The calculation is next extended to the characteristic- free case. We so obtain a \(\mathbf W\)-algebra with fractional divided powers, where \(\mathbf W\) denotes the ring of the big Witt vectors.

MSC:
13K05 Witt vectors and related rings (MSC2000)
14G15 Finite ground fields in algebraic geometry
14L05 Formal groups, \(p\)-divisible groups
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