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For certain tame abelian covers of arithmetic surfaces we obtain formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf and also its square root. These formulas allow us to carry out explicit calculations; in particular, we are able to exhibit examples where these two Euler characteristics and that of the structure sheaf are all different and non-trivial. Our results are obtained by using resolvent techniques...

Erweiterung eines Satzes von Schinzel über Potenzreste

Volker Schulze (1982)

Acta Arithmetica

Existentially closed domains with radical relations.

A. Prestel, J. Schmid (1990)

Journal für die reine und angewandte Mathematik

Explicit construction of integral bases of radical function fields

Qingquan Wu (2010)

Journal de Théorie des Nombres de Bordeaux

We give an explicit construction of an integral basis for a radical function field $K = k (t, ρ)$ , where $ρ^{n} = D \in k [t]$ , under the assumptions $[K : k (t)] = n$ and $c h a r (k) ∤ n$ . The field discriminant of $K$ is also computed. We explain why these questions are substantially easier than the corresponding ones in number fields. Some formulae for the $P$ -signatures of a radical function field are also discussed in this paper.

Explicit forms of Kummer's complementary theorems to his law of quintic reciprocity.

Kenneth S. Williams (1976)

Journal für die reine und angewandte Mathematik

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