相关论文: On the Koszul Betti numbers in positive characteri…

This paper has been withdrawn by the author, due a critical mistake on page 3.

This paper has been withdrawn by the author due to a crucial error in last part of proof.

This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.

This paper has been withdrawn by the author. Much simpler proof of the main result was obtained which led to major changes in the presentation.

Paper has been withdrawn, see comment.

This paper has been withdrawn by the authors due to a fatal flaw in the central proof.

This paper has been withdrawn by the author.

Paper withdrawn because of a gap in the proof of Proposition 3 of Thomas Schick: "Integrality of L2-Betti numbers", Math. Ann. 317, 727-750 (arXiv.org/abs/math.gt/0001101). Most results of the withdrawn paper were based on this proposition.

This paper has been withdrawn by the authors due to an error.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968

The paper has been withdrawn due to an error in the main theorem.

Paper withdrawn. There is a gap in the proof of Proposition 4.3 (its conclusion ``d'o\`{u} la proposition.'' is incorrect). Therefore theorems 1.1 and 3.1, which were the main results of the paper, are not proved.

This paper is withdrawn due to some gaps in the proof

The paper has been withdrawn due to a crucial error in section 3.

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

This paper has been withdrawn by the author due to the presented idea is wrong.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author, due a crucial error in Eq. 6.

This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.