Computing functions on Jacobians and their quotients
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Publication:2942126
DOI10.1112/S1461157015000169zbMath1333.14038arXiv1409.0481OpenAlexW2964117893MaRDI QIDQ2942126
Tony Ezome, Jean-Marc Couveignes
Publication date: 26 August 2015
Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.0481
Theta functions and abelian varieties (14K25) Computational aspects of algebraic curves (14Q05) Isogeny (14K02) Effectivity, complexity and computational aspects of algebraic geometry (14Q20)
Related Items (8)
Fast change of level and applications to isogenies ⋮ Breaking SIDH in polynomial time ⋮ Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields ⋮ Cover attacks for elliptic curves over cubic extension fields ⋮ Cyclic Isogenies for Abelian Varieties with Real Multiplication ⋮ Isogeny graphs of ordinary abelian varieties ⋮ Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with \((\ell ,\ell ,\ell)\)-isogenies ⋮ Computing isogenies between Jacobians of curves of genus 2 and 3
Cites Work
- Computing modular Galois representations
- Linearizing torsion classes in the Picard group of algebraic curves over finite fields
- Computing Riemann-Roch spaces in algebraic function fields and related topics.
- The Weil pairing, and its efficient calculation
- Theta functions on Riemann surfaces
- Counting points on elliptic curves over finite fields
- Computing isogenies between abelian varieties
- Fast algorithms for computing isogenies between elliptic curves
- Asymptotically fast group operations on Jacobians of general curves
- Fast Algorithms for Manipulating Formal Power Series
- Computing separable isogenies in quasi-optimal time
- Computing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves
- Computing low-degree isogenies in genus 2 with the Dolgachev–Lehavi method
- Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
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