P. [. Adams and . Loustaunau, An introduction to Gröbner bases, Graduate Studies in Mathematics, vol.3, 1994.

W. Bosma, J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Journal of Symbolic Computation, vol.24, issue.3-4, pp.235-265, 1997.
DOI : 10.1006/jsco.1996.0125

T. Becker, V. Weispfenning, C. Groebner-bases, H. Birkenhake, . [. Lange et al., Graduate Texts in Mathematics Complex abelian varieties, volume 302 of Grundlehren der Mathematischen Wissenschaften [Fundament al Principles of Gröbner bases, volume 141 of Graduate Texts in Mathematics A computational approach to commutative algebra, Computationnal Approach to Commutative Algebra cooperation with Heinz Kredel. [CL09] R. Carls and D. Lubicz. A p-adic quasi-quadratic time point counting algorithm, pp.698-735, 1993.

D. Cox, J. Little, and D. Shea, Ideals, Varieties and Algorithms Elliptic and modular curves over finite fields and related computational issues, Elk98] N. Elkies Computational perspectives on number theoryFau99] J. C. Faugère. A new efficient algorithm for computing Gröbner bases (F4), pp.21-76, 1992.

J. C. Faugère, A new efficient algorithm for computing Gröbner bases without reduction to zero (F5), Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pp.75-83, 2002.

P. [. Faugère, D. Gianni, T. Lazard, and . Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

G. R. Kempf, Linear Systems on Abelian Varieties, American Journal of Mathematics, vol.111, issue.1, pp.65-94, 1989.
DOI : 10.2307/2374480

D. Kohellaz85 and ]. Lazard, Heegner point lifting algorithm and elliptic curve point counting Ideal Bases and Primary Primary Decomposition:Case of Two Variables, Advances in cryptology?ASIACRYPT 2003, volume 2894 of Lecture Notes in Comput. Sci.Laz92] D. Lazard. Solving zero-dimensional algebraic systems, pp.124-136261, 1985.

R. Lercier and D. Lubicz, A quasi quadratic time algorithm for hyperelliptic curve point counting, The Ramanujan Journal, vol.2, issue.1, pp.399-423, 2006.
DOI : 10.1007/s11139-006-0151-6

URL : https://hal.archives-ouvertes.fr/hal-00456401

D. Lubicz and D. Robert, Efficient Pairing Computation with Theta Functions, 9th International Symposium, 2010.
DOI : 10.1007/978-3-642-14518-6_21

URL : https://hal.archives-ouvertes.fr/hal-00528944

D. Mumford, On the equations defining abelian varieties. I, Inventiones Mathematicae, vol.111, issue.4, pp.287-354, 1966.
DOI : 10.1007/BF01389737

D. Mumford, On the equations defining abelian varieties. II, Inventiones Mathematicae, vol.3, issue.2, pp.75-135, 1967.
DOI : 10.1007/BF01389741

D. Mumford, On the equations defining abelian varieties. II, Inventiones Mathematicae, vol.3, issue.2, pp.75-135, 1967.
DOI : 10.1007/BF01389741

D. Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, issue.5, 1970.

D. Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, issue.5, 1970.

D. Mumford, M. Musili, E. Nori, M. Previato, H. Stillman et al., Jacobian theta functions and differential equations, With the collaboration of C The canonical lift of an ordinary elliptic curve over a finite field and its point counting, Tata lectures on theta II, pp.247-270219, 1984.

F. Vercauteren, B. Preneel, and J. Vandewalle, A Memory Efficient Version of Satoh???s Algorithm, Advances in cryptology?EUROCRYPT 2001 (Innsbruck ), pp.1-13, 2001.
DOI : 10.1007/3-540-44987-6_1