GENUS TWO CURVES WITH EVERYWHERE TWISTED GOOD REDUCTION

We construct examples of genus two curves C over quadratic fields K with everywhere twisted good reduction, i.e., for any finite prime p of K, C has a twist that has good reduction at p. An analogous construction for elliptic curves enables us to recover Setzer's family of curves with everywher...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2013-01, Vol.43 (1), p.55-73, Article 55
Main Authors: BAAZIZ, HOURIA, BOXALL, JOHN
Format: Article
Language:English
Subjects:
11G05
11G30
elliptic curves
everywhere good reduction
Genus two curves
Mathematics
Number Theory
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Summary:We construct examples of genus two curves C over quadratic fields K with everywhere twisted good reduction, i.e., for any finite prime p of K, C has a twist that has good reduction at p. An analogous construction for elliptic curves enables us to recover Setzer's family of curves with everywhere good reduction over an imaginary quadratic field.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2013-43-1-55