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Bad reduction of genus three curves with complex multiplication

Bouw, I., Cooley, J., Lauter, K., Lorenzo Garcia, E., Manes, M., Newton, R. 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


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
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:58167
Publisher Statement:This version may differ from the published version.

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