Abstract
In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.
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Acknowledgements
The authors would like to thank Professor Helmut Lenzing for his lectures about weighted projective lines in Xiamen University in 2011.
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Supported by National Nature Science Foundation of China (Grant Nos. 11571286, 11471269), the Natural Science Foundation of Fujian Province of China (Grant No. 2016J01031) and the Fundamental Research Funds for the Central Universities of China (Grant No. 20720150006)
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Chen, J.M., Chen, J.J. & Lin, Y.N. Prüfer sheaves and generic sheaves over the weighted projective lines and elliptic curves. Acta. Math. Sin.-English Ser. 33, 705–724 (2017). https://doi.org/10.1007/s10114-016-5063-9
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DOI: https://doi.org/10.1007/s10114-016-5063-9