On the relative Wall-Witt groups |
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Authors: | Yongjin Song |
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Affiliation: | (1) Department of Mathematics, Inha University, 402-751 Incheon, Korea |
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Abstract: | LetR* be a simplicial involutive ring. According to certain involutions onK(R*) and ε L R ∗, there are 1/2-local splittings and . It is known [2] that ε L ga α R ∗, the Wall-Witt group. SupposeI→R S is a split extension of discrete involutive rings withI 2=0, andI is a freeS-bimodule. Then we have and . The trace map Tr: Prim n ∧*M(I ⊗ ℚ)→ 0 ρ n ;I ⊗ ℚ) is an isomorphism. We prove in Lemma 1 that the trace map Tr is ℤ/2-equivariant. In Theorem 2 we show that under a certain assumption the rational relative Wall-Witt group vanishes. Theorem 2 can be extended to a more general case (Theorem 3) by employing Goodwillie’s reduction technique [3]. This work was partially supported by KOSEF under Grant 923-0100-010-1. |
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