All Questions
Tagged with complex-multiplication ag.algebraic-geometry
3 questions
11
votes
2
answers
652
views
Abelian variety with prescribed endomorphism ring
Consider the cyclotomic field $L={{\mathbb{Q}}}(\zeta_8)={{\mathbb{Q}}}(\sqrt{2},i)$, where $\zeta_8$ is a primitive 8-th root of unity. Let $\Lambda={{\mathbb{Z}}}[\zeta_8]$ denote the ring of ...
4
votes
2
answers
482
views
abelian varieties with the same CM type are isogenous
Does anybody have a reference for the following fact?
All abelian varieties with complex multiplication and same CM type are isogenous over $\overline{\mathbb{Q}}$?
Here abelian variety with ...
2
votes
1
answer
799
views
Canonical lifts from $\mathbb F_q$ and CM-theory
One knows that (ordinary) Jacobians of hyperelliptic curves over a finite field $\mathbb F_q$ (mostly of genus 1 (elliptic curves) and 2) are extensively studied by cryptographers, as a platform for ...