Timeline for Complex multiplication of Jacobians of quadratic twists of a fixed hyperelliptic curve
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2018 at 12:10 | comment | added | Stanley Yao Xiao | That's what I thought ought to be true (that they are isomorphic over $\overline{\mathbb{Q}}$, but it was only clear to me in the case of elliptic curves. | |
| Apr 24, 2018 at 11:34 | comment | added | Daniel Loughran | $A_C$ and $A_{C_d}$ are isomorphic over $\bar{\mathbb{Q}}$, thus they either both have complex multiplication over $\bar{\mathbb{Q}}$ or neither does. It would help if you clarified your definition of complex multiplication, e.g. whether it takes into account the ground field; for example for elliptic curves the extra endomorphisms are never defined over $\mathbb{Q}$, but only over an imaginary quadratic field. | |
| Apr 24, 2018 at 11:05 | history | asked | Stanley Yao Xiao | CC BY-SA 3.0 |