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Equivariant Euler characteristics and sheaf resolvents

Ph. Cassou-Noguès, M.J. Taylor (2012)

Annales de l’institut Fourier

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...

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 ∈ 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.

Gaussian Integers

Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama (2013)

Formalized Mathematics

Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational number field and a quotient field of the Gaussian integer ring are isomorphic.

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