Journal article
On the determinant bundles of abelian schemes
- Abstract:
- Let π : A → S be an abelian scheme over a scheme S which is quasi-projective over an affine noetherian scheme and let L be a symmetric, rigidified, relatively ample line bundle on A. We show that there is an isomorphism det(π∗L) ⊗24 (π∗ω∨A)⊗12d of line bundles on S, where d is the rank of the (locally free) sheaf π∗L. We also show that the numbers 24 and 12d are sharp in the following sense: if N > 1 is a common divisor of 12 and 24, then there are data as above such that det(π∗L) ⊗(24/N) (π∗ω∨A)⊗(12d/N).
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 181.1KB, Terms of use)
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- Publisher copy:
- 10.1112/S0010437X07003235
Authors
- Publisher:
- Foundation Compositio Mathematica
- Journal:
- Compositio Mathematica More from this journal
- Volume:
- 144
- Issue:
- 02
- Pages:
- 495-502
- Publication date:
- 2008-03-14
- Acceptance date:
- 2007-05-22
- DOI:
- EISSN:
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1570-5846
- ISSN:
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0010-437X
- Keywords:
- Pubs id:
-
pubs:745044
- UUID:
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uuid:e8d70611-14cd-4981-ab53-e1842165aa5a
- Local pid:
-
pubs:745044
- Source identifiers:
-
745044
- Deposit date:
-
2018-05-05
Terms of use
- Copyright holder:
- Foundation Compositio Mathematica
- Copyright date:
- 2008
- Notes:
- COPYRIGHT: © Foundation Compositio Mathematica 2008. This is the accepted manuscript version of the article. The final version is available online from Foundation Compositio Mathematica at: https://doi.org/10.1112/S0010437X07003235
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