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Relative Cartier divisors and Laurent polynomial extensions

Relative Cartier divisors and Laurent polynomial extensions 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 ] ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Relative Cartier divisors and Laurent polynomial extensions

Mathematische Zeitschrift , Volume 285 (2) – Jun 16, 2016

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-016-1710-1
Publisher site
See Article on Publisher Site

Abstract

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 ] ) .

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jun 16, 2016

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