Computing separable isogenies in quasi-optimal time

@article{Lubicz2014ComputingSI,
  title={Computing separable isogenies in quasi-optimal time},
  author={D. Lubicz and Damien Robert},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
Let $A$ be an abelian variety of dimension $g$ together with a principal polarization $\phi: A \rightarrow \hat{A}$ defined over a field $k$. Let $\ell$ be an odd integer prime to the characteristic of $k$ and let $K$ be a subgroup of $A[\ell]$ which is maximal isotropic for the Riemann form associated to $\phi$. We suppose that $K$ is defined over $k$ and let $B=A/K$ be the quotient abelian variety together with a polarization compatible with $\phi$. Then $B$, as a polarized abelian variety… Expand

References

SHOWING 1-10 OF 40 REFERENCES
Computing modular correspondences for abelian varieties
Computing isogenies between abelian varieties
Equations Defining Abelian Varieties
Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
Modular polynomials via isogeny volcanoes
Computing Hilbert class polynomials with the Chinese remainder theorem
Efficient Pairing Computation with Theta Functions
Complex Abelian Varieties
Computing the endomorphism ring of an ordinary elliptic curve over a finite field
...
1
2
3
4
...