E. A. Arnold, Modular algorithms for computing Gr??bner bases, Journal of Symbolic Computation, vol.35, issue.4, pp.403-419, 2003.
DOI : 10.1016/S0747-7171(02)00140-2

URL : http://doi.org/10.1016/s0747-7171(02)00140-2

F. Michael, I. G. Atiyah, and . Macdonald, Introduction to commutative algebra, 1969.

D. Bayer and D. Mumford, What can be computed in algebraic geometry? Eisenbud Computational algebraic geometry and commutative algebra, 1991.

C. Bertone, The Euler characteristic as a polynomial in the Chern classes, Int. J. Algebra, vol.2, pp.13-16757, 2008.

C. Bertone, G. Chèze, and A. Galligo, Modular Las Vegas Algorithms for Polynomial Absolute Factorization Available on http, 2009.

C. Bertone and M. Roggero, Positivity of Chern classes for reflexive sheaves on P N, Geometriae Dedicata, vol.260, issue.3, pp.121-138, 2009.
DOI : 10.1007/s10711-009-9362-5

C. Bertone and M. Roggero, Splitting type, global sections and Chern classes for vector bundles on P N, J. Korean Math. Soc

A. Bostan, G. Lecerf, B. Salvy, É. Schost, and B. Wiebelt, Complexity issues in bivariate polynomial factorization, Proceedings of the 2004 international symposium on Symbolic and algebraic computation , ISSAC '04, pp.42-49, 2004.
DOI : 10.1145/1005285.1005294

URL : https://hal.archives-ouvertes.fr/hal-00186759

L. Richard, J. D. Burden, and . Faires, Numerical analysis, p.768, 1993.
URL : https://hal.archives-ouvertes.fr/hal-01500827

G. Castelnuovo, Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica, Rendiconti del Circolo Matematico di Palermo, vol.7, issue.S1, 1893.
DOI : 10.1007/BF03012436

M. Chardin, Cohomology of projective schemes: from annihilators to vanishing, Journal of Algebra, vol.274, issue.1, pp.68-79, 2004.
DOI : 10.1016/j.jalgebra.2003.10.008

URL : https://hal.archives-ouvertes.fr/hal-00137093

M. Chardin and P. Philippon, Regularity and interpolation. (Régularité et interpolation .), J. Algebr. Geom, vol.8, issue.3, pp.471-481, 1999.

M. Chardin and B. Ulrich, Liaison and Castelnuovo-Mumford regularity, American Journal of Mathematics, vol.124, issue.6, pp.1103-1124, 2002.
DOI : 10.1353/ajm.2002.0035

URL : https://hal.archives-ouvertes.fr/hal-00137105

G. Chèze, Des méthodes symboliques-numériques et exactes pour la factorisation absolue des polynômes en deux variables, 2004.

G. Chèze and A. Galligo, Four lectures on polynomial absolute factorization Solving polynomial equations. Foundations, algorithms, and applications, Algorithms and Computation in Mathematics, vol.14, pp.339-392, 2005.

G. Chèze and G. Lecerf, Lifting and recombination techniques for absolute factorization, Journal of Complexity, vol.23, issue.3, pp.380-420, 2007.
DOI : 10.1016/j.jco.2007.01.008

F. Cioffi, M. G. Marinari, and L. Ramella, Regularity bounds by minimal generators and Hilbert function, Collectanea mathematica, vol.141, issue.1, pp.89-100, 2009.
DOI : 10.1007/BF03191218

H. Cohen, F. Diaz, and . Diaz, A polynomial reduction algorithm, Journal de Th??orie des Nombres de Bordeaux, vol.3, issue.2, pp.351-360, 1991.
DOI : 10.5802/jtnb.55

D. Cox, J. Little, and D. O. Shea, Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra, 1996.

P. Dèbes and Y. Walkowiak, Bounds for Hilbert's Irreducibility Theorem, Pure and Applied Mathematics Quarterly, vol.4, issue.4, pp.1059-1083, 2008.
DOI : 10.4310/PAMQ.2008.v4.n4.a4

W. Decker, G. Greuel, and G. Pfister, Primary Decomposition: Algorithms and Comparisons, Algorithmic algebra and number theory, pp.187-220, 1997.
DOI : 10.1007/978-3-642-59932-3_10

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

W. Decker and C. Lossen, Computing in algebraic geometry. A quick start using SINGULAR, Algorithms and Computation in Mathematics, vol.16, 2006.

C. Durvye, Evaluation techniques for zero-dimensional primary decomposition, Journal of Symbolic Computation, vol.44, issue.9, pp.1089-1113, 2009.
DOI : 10.1016/j.jsc.2008.02.008

URL : https://hal.archives-ouvertes.fr/hal-00682079

R. Dvornicich and C. Traverso, Newton symmetric functions and the arithmetic of algebraically closed fields, Proc. 5th Int. Conference, AAECC-5, pp.216-224, 1987.
DOI : 10.1007/3-540-51082-6_79

D. Eisenbud, Commutative algebra. With a view toward algebraic geometry. Graduate Texts in Mathematics, 1995.

R. P. Helaman, D. H. Ferguson, S. Bailey, and . Arno, Analysis of PSLQ, an integer relation finding algorithm, Math. Comput, vol.68, issue.225, pp.351-369, 1999.

W. Fulton, Intersection theory, 1998.

A. Galligo, A propos du th??or??me de pr??paration de weierstrass, Lect. Notes Math, vol.130, pp.543-579, 1970.
DOI : 10.1090/S0002-9947-1968-0217093-3

A. Galligo and D. Rupprecht, Irreducible Decomposition of Curves, Journal of Symbolic Computation, vol.33, issue.5, pp.661-677, 2002.
DOI : 10.1006/jsco.2000.0528

S. Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, Journal of Algebra, vol.237, issue.2, pp.501-520, 2001.
DOI : 10.1006/jabr.2000.8586

K. O. Geddes, S. R. Czapor, and G. Labahn, Algorithms for computer algebra, 1992.
DOI : 10.1007/b102438

P. Gianni, B. Trager, and G. Zacharias, Gr??bner bases and primary decomposition of polynomial ideals, Journal of Symbolic Computation, vol.6, issue.2-3, pp.149-167, 1988.
DOI : 10.1016/S0747-7171(88)80040-3

M. Giusti, J. Heintz, J. E. Morais, and L. M. Pardo, When polynomial equation systems can be ???solved??? fast?, 11th international symposium, pp.205-231, 1995.
DOI : 10.1007/3-540-60114-7_16

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

Q. Fernando and . Gouvêa, p-adic numbers. An introduction, 1993.

L. Mark and . Green, Generic initial ideals Six lectures on commutative algebra. Lectures presented at the summer school, Basel: Birkhäuser. Prog. Math, vol.166, pp.119-186, 1996.

G. Greuel, G. Pfister, and H. Schönemann, SINGULAR 3-1-0 ? A computer algebra system for polynomial computations, 2009.

L. Gruson, R. Lazarsfeld, and C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves, Inventiones Mathematicae, vol.206, issue.3, pp.491-506, 1983.
DOI : 10.1007/BF01398398

L. Gruson and C. Peskine, Section plane d'une courbe gauche: Postulation. Enumerative geometry and classical algebraic geometry, Prog. Math, vol.24, pp.33-35, 1982.
DOI : 10.1007/978-1-4684-6726-0_2

R. Hartshorne, Stable reflexive sheaves, Mathematische Annalen, vol.47, issue.2, pp.121-176, 1980.
DOI : 10.1007/BF01467074

URL : http://www.digizeitschriften.de/download/PPN235181684_0254/PPN235181684_0254___log17.pdf

R. Hartshorne, Algebraic geometry. Corr. 3rd printing, Graduate Texts in Mathematics, vol.52, 1983.

G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Mathematische Annalen, vol.95, issue.1, pp.736-788, 1926.
DOI : 10.1007/BF01206635

K. Loo and . Hua, Introduction to number theory. Transl. from the Chinese by Peter Shiu, 1982.

A. Joux and J. Stern, Lattice reduction, J. Cryptology, vol.11, issue.3, pp.161-185, 1998.
DOI : 10.1201/9781420070033.ch10

E. Kaltofen, Fast parallel absolute irreducibility testing, Journal of Symbolic Computation, vol.1, issue.1, pp.57-67, 1985.
DOI : 10.1016/S0747-7171(85)80029-8

URL : http://doi.org/10.1016/s0747-7171(85)80029-8

E. Kaltofen, Polynomial factorization 1982-1986 Computers and mathematics, Proc. Int. Conf., Stanford/CA (USA) 1986, pp.285-309, 1990.

E. Kaltofen, Polynomial factorization 1987???1991, Proc. LATIN '92, 1992.
DOI : 10.1007/BFb0023837

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

R. Kannan, A. K. Lenstra, and L. Lovász, Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers, Mathematics of Computation, vol.50, issue.181, pp.235-250, 1988.
DOI : 10.1090/S0025-5718-1988-0917831-4

P. Kornerup and R. T. Gregory, Mapping integers and hensel codes onto Farey fractions, BIT, vol.81, issue.1, pp.9-20, 1983.
DOI : 10.1007/BF01937322

URL : http://ojs.statsbiblioteket.dk/index.php/daimipb/article/download/7423/6274

M. Kreuzer and L. Robbiano, Computational commutative algebra. II, 2005.
DOI : 10.1007/978-3-540-70628-1

L. Olav-arnfinn, A generalized trisecant lemma, Proc., Tromso Symp, pp.112-149, 1977.

G. Lecerf, Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers, Journal of Complexity, vol.19, issue.4, pp.564-596, 2003.
DOI : 10.1016/S0885-064X(03)00031-1

URL : https://hal.archives-ouvertes.fr/hal-00186727

G. Lecerf, Sharp precision in Hensel lifting for bivariate polynomial factorization, Mathematics of Computation, vol.75, issue.254, pp.921-933, 2006.
DOI : 10.1090/S0025-5718-06-01810-2

URL : https://hal.archives-ouvertes.fr/hal-00186733

K. Arjen, H. W. Lenstra, L. Lenstra, and . Lovász, Factoring polynomials with rational coefficients, Math. Ann, vol.261, pp.515-534, 1982.

E. Mezzetti, Differential-geometric methods for the lifting problem and linear systems on plane curves, J. Algebr. Geom, vol.3, issue.3, pp.375-398, 1994.

E. Mezzetti and I. Raspanti, A Laudal-type theorem for surfaces in P 4, Rend. Semin. Mat, vol.48, issue.4, pp.529-537, 1990.

D. J. Mumford, Lectures on curves on an algebraic surface, 1966.

Q. Phong, D. Nguên, and . Stehlé, Floating-point LLL revisited, Advances in cryptology ? EUROCRYPT 2005. 24th annual international conference on the theory and applications of cryptographic techniques, pp.215-233, 2005.

E. Noether, Ein algebraisches Kriterium f???r absolute Irreduzibilit???t, Mathematische Annalen, vol.85, issue.1, pp.26-33, 1922.
DOI : 10.1007/BF01449599

A. Novocin and M. Van-hoeij, Gradual sub-lattice reduction and a new complexity for factoring polynomials. to appear in Gradual sub-lattice reduction and a new complexity for factoring polynomials -LATIN, 2010.
URL : https://hal.archives-ouvertes.fr/ensl-00452881

C. Okonek, M. Schneider, and H. Spindler, Vector bundles on complex projective spaces, Progress in Mathematics, vol.3, 1980.
DOI : 10.1007/978-3-0348-0151-5

A. Markowich and O. , On multiplication and factorization of polynomials . I: Lexicographic orderings and extreme aggregates of terms, Aequationes Math, vol.13, pp.201-228, 1975.

F. Pauer, On lucky ideals for Gr??bner basis computations, Journal of Symbolic Computation, vol.14, issue.5, pp.471-482, 1992.
DOI : 10.1016/0747-7171(92)90018-Y

J. Ragot, Sur la factorisation absolue des polynomes, 1997.

. Jean-francois and . Ragot, Probabilistic absolute irreducibility test for polynomials, J. Pure Appl. Algebra, vol.172, issue.1, pp.87-107, 2002.

M. Roggero, Lifting problem for codimension two subvarieties in P n+2 : border cases Geometric and combinatorial aspects of commutative algebra. Papers based on lectures delivered at the international conference on commutative algebra and algebraic geometry, Lect. Notes Pure Appl. Math, vol.217, pp.309-326, 1999.

D. Rupprecht, Semi-numerical absolute factorization of polynomials with integer coefficients, Journal of Symbolic Computation, vol.37, issue.5, pp.557-574, 2004.
DOI : 10.1016/S0747-7171(02)00011-1

W. M. Schmidt, Equations over finite fields. An elementary approach, Lecture Notes in Mathematics, vol.536, 1976.
DOI : 10.1007/BFb0080437

R. Schneider, Convex bodies: the Brunn-Minkowski theory. Encyclopedia of Mathematics and Its Applications. 44. Cambridge, 1993.

C. Peter and S. , Fast LLL-type lattice reduction, Inf. Comput, vol.204, issue.1, pp.1-25, 2006.

J. Andrew, J. Sommese, and . Verschelde, Numerical homotopies to compute generic points on positive dimensional algebraic sets, J. Complexity, vol.16, issue.3, pp.572-602, 2000.

J. S. Andrew, C. W. Verschelde, and . Wampler, Numerical decomposition of the solution sets of polynomial systems into irreducible components, SIAM J. Numer. Anal, vol.38, issue.6, pp.2022-2046, 2001.

J. Andrew, C. W. Sommese, and . Wampler, Numerical algebraic geometry The mathematics of numerical analysis. 1995 AMS-SIAM summer seminar in applied mathematics, Lect. Appl. Math, vol.32, pp.749-763, 1995.

P. Stevenhagen and H. W. Jun-lenstra, Chebotar??v and his density theorem, The Mathematical Intelligencer, vol.9, issue.4, pp.26-37, 1996.
DOI : 10.1007/BF03027290

R. Strano, Sulle sezione iperpiane dele curve, Milan Journal of Mathematics, vol.57, issue.6, pp.125-134, 1987.
DOI : 10.1007/bf02925046

A. Tortora, On the lifting problem in codimension two, Matematiche, vol.52, issue.1, pp.41-51, 1997.

B. Trager, On the integration of algebraic functions, 1985.

B. Trager, Good reduction of curves and applications, Meeting on Computer and Commutative Algebra (COCOA II), 1989.

M. Valenzano, Bounds on the degree of two-codimensional integral varieties in projective space, Journal of Pure and Applied Algebra, vol.158, issue.1, pp.111-122, 2001.
DOI : 10.1016/S0022-4049(00)00027-X

J. Von, Z. Gathen, and J. Gerhard, Modern computer algebra, 2003.

F. Winkler, A p-adic approach to the computation ofGr??bner bases, Journal of Symbolic Computation, vol.6, issue.2-3, pp.287-304, 1988.
DOI : 10.1016/S0747-7171(88)80049-X

Y. Chee-keng, Fundamental problems of algorithmic algebra, 2000.

U. Zannier, On the reduction modulo p of an absolutely irreducible polynomial f (x, y), Archiv der Mathematik, vol.56, issue.2, pp.129-138, 1997.
DOI : 10.1007/s000130050041