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An analogue of Pfister's local-global principle in the burnside ring

Martin Epkenhans (1999)

Journal de théorie des nombres de Bordeaux

Let N / K be a Galois extension with Galois group 𝒢 . We study the set 𝒯 ( 𝒢 ) of -linear combinations of characters in the Burnside ring ( 𝒢 ) which give rise to -linear combinations of trace forms of subextensions of N / K which are trivial in the Witt ring W ( K ) of K . In particular, we prove that the torsion subgroup of ( 𝒢 ) / 𝒯 ( 𝒢 ) coincides with the kernel of the total signature homomorphism.

Dualization in algebraic K-theory and the invariant e¹ of quadratic forms over schemes

Marek Szyjewski (2011)

Fundamenta Mathematicae

In the classical Witt theory over a field F, the study of quadratic forms begins with two simple invariants: the dimension of a form modulo 2, called the dimension index and denoted e⁰: W(F) → ℤ/2, and the discriminant e¹ with values in k₁(F) = F*/F*², which behaves well on the fundamental ideal I(F)= ker(e⁰). Here a more sophisticated situation is considered, of quadratic forms over a scheme and, more generally, over an exact category with duality. Our purposes are: ...

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