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If $$i:A\subset B$$ i : A ⊂ B is a commutative ring extension, we show that the group $${\mathcal I}(A,B)$$ I ( A , B ) of invertible A-submodules of B is contracted in the sense of Bass, with $$L{\mathcal I}(A,B)=H^0_{\mathrm {et}}(A,i_*{\mathbb Z}/{\mathbb Z})$$ L I ( A , B ) = H et 0 ( A , i ∗ Z / Z ) . This gives a canonical decomposition for $${\mathcal I}(A[t,\frac{1}{t}],B[t,\frac{1}{t}])$$ I ( A [ t , 1 t ] , B [ t , 1 t ] ) .
Mathematische Zeitschrift – Springer Journals
Published: Jun 16, 2016
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