Conjugated ethylene-vinyl ester copolymer, with a molar mass of over 10,000 g.mol -1 containing: a) an ethylene-derived group of structure A - (CH 2 -CH 2) n in which n is a whole number of between 45 to 650; b) at least one group of structure B: - (CH 2 -CHOCOR 1) m-x - in which m is a whole number of between 5 to 110, and R 1 is at least one residue selected from the groups of linear or branched alkyl groups, C 1 -C 15; c) one group of structure C: - (CH 2 -CHOH) x1 - in which x 1 ranges from 0 to 0.95 x; d) at least one group of structure D: - (CH 2 -CHG) x2 - or of structure D' -CH 2 C(OCOCH3)Q) x2 - in which x 2 is never 0 and ranges from 0.05 x to x, preferably x 2 is x, and G corresponds to a group of structure G1 or G2 or G3 where G1 corresponds to the structure -OCOCHCH 3 Q- G2 corresponds to the structure -OCOCH 2 Q- G3 corresponds to the structure -OCOCH 2 SQ- in which Q corresponds to - either a group of structure Q1 -(CH 2 -CZCOOR q1) p1 -X q in which p 1 ranges from 1 to 800; - or a group of structure Q2 -(CH 2 -CZOCOR q2) p2 -X q in which p 2 ranges from 1 to 100; in which X corresponds to a halogen atom, preferably Br or I, q ranges from 0 to 1, Z corresponds to a hydrogen atom or a CH 3 group, and R q1 or R q2 corresponds to a linear or branched alkyl group, either saturated or unsaturated, C 1 -C 30, preferably C 4 -C 15, advantageously C 6 -C 15 and more advantageously still C 6 -C 12, and more particularly 2-ethylhexylacrylate, copolymer in which x = x 1 + x 2 and x ranges from 0.25 to 55; the molar percentage of A groups in the polymer is 29-97% in moles; the molar percentage of B groups in the polymer is 1-20% in moles; the molar percentage of C groups in the polymer is 0-10% in moles; the molar percentage of D or D' groups in the polymer is 0.6-64% in moles and the molar percentage of Q in D or D' is de 8.2-99.9% in moles. a) an ethylene-derived group of structure A - (CH 2 -CH 2) n in which n is a whole number of between 45 to 650; b) at least one group of structure B: - (CH 2 -CHOCOR 1) m-x - in which m is a whole number of between 5 to 110, and R 1 is at least one residue selected from the groups of linear or branched alkyl groups, C 1 -C 15; c) one group of structure C: - (CH 2 -CHOH) x1 - in which x 1 ranges from 0 to 0.95 x; d) at least one group of structure D: - (CH 2 -CHG) x2 - or of structure D' -CH 2 C(OCOCH3)Q) x2 - in which x 2 is never 0 and ranges from 0.05 x to x, preferably x 2 is x, and G corresponds to a group of structure G1 or G2 or G3 where G1 corresponds to the structure -OCOCHCH 3 Q- G2 corresponds to the structure -OCOCH 2 Q- G3 corresponds to the structure -OCOCH 2 SQ- in which Q corresponds to - either a group of structure Q1 -(CH 2 -CZCOOR q1) p1 -X q in which p 1 ranges from 1 to 800; - or a group of structure Q2 -(CH 2 -CZOCOR q2) p2 -X q in which p 2 ranges from 1 to 100; in which X corresponds to a halogen atom, preferably Br or I, q ranges from 0 to 1, Z corresponds to a hydrogen atom or a CH 3 group, and R q1 or R q2 corresponds to a linear or branched alkyl group, either saturated or unsaturated, C 1 -C 30, preferably C 4 -C 15, advantageously C 6 -C 15 and more advantageously still C 6 -C 12, and more particularly 2-ethylhexylacrylate, copolymer in which x = x 1 + x 2 and x ranges from 0.25 to 55; the molar percentage of A groups in the polymer is 29-97% in moles; the molar percentage of B groups in the polymer is 1-20% in moles; the molar percentage of C groups in the polymer is 0-10% in moles; the molar percentage of D or D' groups in the polymer is 0.6-64% in moles and the molar percentage of Q in D or D' is de 8.2-99.9% in moles. G1 corresponds to the structure -OCOCHCH 3 Q- G2 corresponds to the structure -OCOCH 2 Q- G3 corresponds to the structure -OCOCH 2 SQ- - either a group of structure Q1 -(CH 2 -CZCOOR q1) p1 -X q in which p 1 ranges from 1 to 800; - or a group of structure Q2 -(CH 2 -CZOCOR q2) p2 -X q in which p 2 ranges from 1 to 100; in which X corresponds to a halogen atom, preferably Br or I, q ranges from 0 to 1, Z corresponds to a hydrogen atom or a CH 3 group, and R q1 or R q2 corresponds to a linear or branched alkyl group, either saturated or unsaturated, C 1 -C 30, preferably C 4 -C 15, advantageously C 6 -C 15 and more advantageously still C 6 -C 12, and more particularly 2-ethylhexylacrylate,