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Relative Cartier divisors and Laurent polynomial extensions

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Abstract

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

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Acknowledgments

The first author would like to express his sincere thanks to Balwant Singh for many fruitful discussions and for his guidance, and to D. S. Nagaraj for useful discussion.

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Authors and Affiliations

  1. Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, Chennai, Tamil Nadu, 600113, India

    Vivek Sadhu

  2. Mathematics Department, Rutgers University, New Brunswick, NJ, 08901, USA

    Charles Weibel

Authors
  1. Vivek Sadhu
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  2. Charles Weibel
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Corresponding author

Correspondence to Charles Weibel.

Additional information

Sadhu was supported by IMSC, Chennai Postdoctoral Fellowship.

Weibel was supported by NSF grants.

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Sadhu, V., Weibel, C. Relative Cartier divisors and Laurent polynomial extensions. Math. Z. 285, 353–366 (2017). https://doi.org/10.1007/s00209-016-1710-1

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  • DOI: https://doi.org/10.1007/s00209-016-1710-1

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