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Bad reduction of genus $3$ curves with complex multiplication
- Publication Year :
- 2014
-
Abstract
- 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 $\mathfrak{p}$ of $M$ such that the stable reduction of $C$ at $\mathfrak{p}$ contains three irreducible components of genus $1$.
- Subjects :
- Mathematics - Number Theory
Mathematics - Algebraic Geometry
11G15, 14K22, 15B33
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1407.3589
- Document Type :
- Working Paper