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Bad reduction of genus three curves with complex multiplication

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Bouw, I., Cooley, J., Lauter, K., Lorenzo Garcia, E., Manes, M., Newton, R. ORCID: https://orcid.org/0000-0003-4925-635X and Ozman, E. (2015) Bad reduction of genus three curves with complex multiplication. In: Bertin, M. J., Bucur, A., Feigon, B. and Schneps, L. (eds.) Women in Numbers Europe: Research Directions in Number Theory. Association for Women in Mathematics Series, 2 (2364-5733). Springer, pp. 109-151. ISBN 9783319179865

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To link to this item DOI: 10.1007/978-3-319-17987-2

Abstract/Summary

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.

Item Type:Book or Report Section
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:58167
Publisher:Springer
Publisher Statement:This version may differ from the published version.
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