Efficient algorithms for abelian varieties and their moduli spaces Page 1 HAL Id: tel-03498268
https://hal.science/tel-03498268 Submitted on 20 Dec 2021 HAL is a multi-disciplinary open …

Jacobi's $\theta $ function has numerous applications in mathematics and computer
science; a naive algorithm allows the computation of $\theta (z,\tau) $, for $ z,\tau $ verifying …

We outline an algorithm to compute θ (z, τ) in genus two in quasi-linear time, borrowing
ideas from the algorithm for theta constants and the one for θ (z, τ) in genus one. Our …

Counting points on algebraic curves has drawn a lot of attention due to its many applications
from number theory and arithmetic geometry to cryptography and coding theory. In this …

Fix a prime number ℓ ℓ. Graphs of isogenies of degree a power of ℓ ℓ are well-understood for
elliptic curves, but not for higher-dimensional abelian varieties. We study the case of …

We describe an evaluation/interpolation approach to compute modular polynomials on a
Hilbert surface, which parametrizes abelian surfaces with maximal real multiplication. Under …

We propose to generalize the work of Régis Dupont for computing modular polynomials in
dimension to new invariants. We describe an algorithm to compute modular polynomials for …

We analyze complex multiplication for Jacobians of curves of genus 3, as well as the
resulting Shimura class groups and their subgroups corresponding to Galois conjugation …

Up to isomorphism, every three-dimensional simple principally polarized abelian variety
over ℂ is the Jacobian of a smooth projective curve of genus 3. Furthermore, this curve is …

We give an explicit version of Shimura's reciprocity law for singular values of Siegel modular
functions. We use this to construct the first examples of class invariants of quartic CM fields …