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2.– Kiran Kedlaya spotted an error in the published version of the proof of Theorem 5.2 and provided a correction which led to an improved statement

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1.– Nicolas Addington pointed out to us that the example in Section 5.4.2 of the published version is wrong. The equation should be

x31+x32+x33+x21x2+x22x3+x2x4x5+x23x1+x1x2x3+x1x24+x21x4+x2x25+x22x5 +x24x5+x4x25+x3x26+x23x6+x24x6 +x4x26+x25x6+x5x26+x4x5x6 = 0.

It defines a smooth cubic fourfold X ⊂ P5F2, the only F2-line contained in X is the line h(0,0,0,0,1,1),(0,0,0,1,0,1)i, and X contains 13 F2-points.

2.– Kiran Kedlaya spotted an error in the published version of the proof of Theorem 5.2 and provided a correction which led to an improved statement. He also kindly provided Proposition 5.5 and its proof.

3.–Daniel Bragg spotted an error in the published version of the statement of Theorem 4.11:

in the case p≡1 (mod 3) andn = 4, one has

Pn0(XFnp, T) = (1−p(a2−2p)T +p4T2)(1−p2T)20.

4.– Equation (5) in the published version should be

Q1(Y, T) =T2m+a1T2m−1 +· · ·+am−1Tm+1+amTm+qam−1Tm−1+· · ·+qm−1a1T +qm.

The arxiv version (which is a slightly expanded version of the published text) include corrections of all the points mentioned above.

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