Related papers: The Boltzmann-Sinai Ergodic Hypothesis for Hard Ba…

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2080.

The authors have decided to withdraw this submission. Clarifications/corrections, if any, may follow at a later date.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

This paper has been withdrawn due to disagreement of suggested results and methods between authors.

This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.

This paper has been withdrawn.

This paper has been withdrawn by the author due to a crucial error in the Proof of Theorem 0.3

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

This paper has been withdrawn by the author due to the inaccurate result.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the author due to crucial sign error in Lemma 8.1.

This paper has been withdrawn by the author(s), due a crucial sign error in Eqn. 1.

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This paper has been withdrawn

This paper has been withdrawn.

This paper has been withdrawn by the authors due to an error in the main theorem.

This paper has been withdrawn by the author.