Witt Vectors and a Question of Keating and Rudnick
نویسنده
چکیده
Following Keating and Rudnick, we say that a character Λ : B× → C× is “even” if it is trivial on the subgroup k×. The quotient group B×/k× is the group of “big” Witt vectors mod X with values in k. Recall that for any ringA, the groupBigWitt(A) is simply the abelian group 1 +XA[[X]] of formal series with constant term 1, under multiplication of formal series. In this group, the elements 1 +XA[[X]] form a subgroup; the quotient by this subgroup is BigWittn(A): BigWittn(A) := (1 +XA[[X]])/(1 +X A[[X]]). We will restrict this functor A 7→ BigWittn(A) to variable k-algebras A. In this way, BigWittn becomes a commutative unipotent groupscheme over k. The Lang torsor construction
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