L. M. Adleman and M. Huang, Counting Points on Curves and Abelian Varieties Over Finite Fields, Journal of Symbolic Computation, vol.32, issue.3, pp.171-189, 2001.
DOI : 10.1006/jsco.2001.0470

URL : https://doi.org/10.1006/jsco.2001.0470

A. O. Atkin and F. Morain, Finding suitable curves for the elliptic curve method of factorization, Mathematics of Computation, vol.60, issue.201, pp.399-405, 1993.
DOI : 10.1090/S0025-5718-1993-1140645-1

URL : https://hal.archives-ouvertes.fr/inria-00075015

A. Cafure and G. Matera, Fast computation of a rational point of a variety over a finite field, Mathematics of Computation, vol.75, issue.256, pp.2049-2085, 2006.
DOI : 10.1090/S0025-5718-06-01878-3

D. G. Cantor, Computing in the Jacobian of a hyperelliptic curve, Mathematics of Computation, vol.48, issue.177, pp.95-101, 1987.
DOI : 10.1090/S0025-5718-1987-0866101-0

D. G. Cantor, On the analogue of the division polynomials for hyperelliptic curves, Journal fur die reine und angewandte Mathematik, pp.91-146, 1994.

H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange et al., Handbook of elliptic and hyperelliptic curve cryptography, 2005.
DOI : 10.1201/9781420034981

S. D. Galbraith, Mathematics of public key cryptography, 2012.
DOI : 10.1017/CBO9781139012843

P. Gaudry, D. R. Kohel, and B. A. Smith, Counting Points on Genus 2 Curves with Real Multiplication, ASIACRYPT 2011, pp.504-519, 2011.
DOI : 10.1007/978-3-642-25385-0_27

URL : https://hal.archives-ouvertes.fr/inria-00598029

P. Gaudry and É. Schost, Genus 2 point counting over prime fields, Journal of Symbolic Computation, vol.47, issue.4, pp.368-400, 2012.
DOI : 10.1016/j.jsc.2011.09.003

URL : https://hal.archives-ouvertes.fr/inria-00542650

M. Giusti, G. Lecerf, and B. Salvy, A Gr??bner Free Alternative for Polynomial System Solving, Journal of Complexity, vol.17, issue.1, pp.154-211, 2001.
DOI : 10.1006/jcom.2000.0571

URL : https://doi.org/10.1006/jcom.2000.0571

D. Harvey, Computing zeta functions of arithmetic schemes, Proceedings of the London Mathematical Society, pp.1379-1401, 2015.
DOI : 10.1112/S1461157012001179

URL : http://arxiv.org/pdf/1402.3439.pdf

J. Heintz, Definability and fast quantifier elimination in algebraically closed fields, Theoretical Computer Science, vol.24, issue.3, pp.239-277, 1983.
DOI : 10.1016/0304-3975(83)90002-6

URL : https://doi.org/10.1016/0304-3975(83)90002-6

M. Huang and D. Ierardi, Counting Points on Curves over Finite Fields, Journal of Symbolic Computation, vol.25, issue.1, pp.1-21, 1998.
DOI : 10.1006/jsco.1997.0164

URL : https://doi.org/10.1006/jsco.1997.0164

K. S. Kedlaya, Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, Journal of the Ramanujan mathematical society, vol.16, issue.4, pp.323-338, 2001.

S. L. Kleiman, Bertini and his two fundamental theorems. ArXiv e-print alg- geom/9704018v1, 1997.

A. G. Lauder, Deformation theory and the computation of zeta functions, Proceedings of the London Mathematical Society, pp.565-602, 2004.
DOI : 10.1112/S0024611503014461

URL : http://plms.oxfordjournals.org/cgi/reprint/88/3/565.pdf

A. G. Lauder and D. Wan, Counting points on varieties over finite fields of small characteristic, Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography, Mathematical Sciences Research Institute Publications, pp.579-612, 2008.

D. Lorenzini, An invitation to arithmetic geometry, Graduate Studies in Mathematics, vol.9, 1996.
DOI : 10.1090/gsm/009

D. Mumford, Abelian varieties, 1974.

J. Pila, Frobenius maps of abelian varieties and finding roots of unity in finite fields, Mathematics of Computation, vol.55, issue.192, pp.745-763, 1990.
DOI : 10.1090/S0025-5718-1990-1035941-X

URL : http://www.ams.org/mcom/1990-55-192/S0025-5718-1990-1035941-X/S0025-5718-1990-1035941-X.pdf

J. Pila, Counting points on curves over families in polynomial time. ArXiv e-print math/0504570v1, 2005.

M. Safey-el-din and É. Schost, A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets, Journal of the ACM, vol.63, issue.6, pp.1-48, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00849057

T. Satoh, The canonical lift of an ordinary elliptic curve over a finite field and its point counting, Journal of the Ramanujan mathematical society, vol.15, issue.4, pp.247-270, 2000.

R. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Mathematics of Computation, vol.44, issue.170, pp.483-494, 1985.
DOI : 10.2307/2007968

A. J. Sommese, C. W. Wampler, and I. , The numerical solution of systems of polynomials arising in engineering and science, World Scientific, 2005.
DOI : 10.1142/5763

G. Tenenbaum, Introduction to analytic and probabilistic number theory, 1995.
DOI : 10.1090/gsm/163

URL : https://hal.archives-ouvertes.fr/hal-01281339

J. Tuitman, Counting points on curves using a map to $\mathbf {P}^1$, Mathematics of Computation, vol.85, issue.298, pp.961-981, 2016.
DOI : 10.1090/mcom/2996

J. Tuitman, Counting points on curves using a map to P 1 II. Finite Fields and Their Applications, p.301, 2017.
DOI : 10.1016/j.ffa.2016.12.008

URL : http://arxiv.org/pdf/1412.7217

J. , V. Zur-gathen, and J. Gerhard, Modern computer algebra, 2013.