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

This paper has been withdrawn by the authors due to a crucial gap in the estimates for m>=4.

After receiving useful peer comments, we would like to withdraw this paper.

This paper has been withdrawn by the author due to inconsistency of the considered working hypothesis. The consistent treatment is presented in the last publications of the author.

We correct the proofs of the main theorems in our paper "Limit theorems for Betti numbers of random simplicial complexes".

This paper has been withdrawn by the authors, due to an error in the proof of Lemma 3.1.

This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.

This paper has been withdrawn by the author since the proof of Lemma 8 is not correct.

This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.

This paper has been withdrawn by the author due to its publication

This paper has been withdrawn by the authors due to numerical problems to get viable results.

This paper has been withdrawn by the authors due to the crucial wrong assumption following Eq. 9.

This paper is withdrawn. See quant-ph/9806031 for a discussion.

This paper has been withdrawn by the author due to an error in the proof of Theorem 1.

The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.

This paper has been withdrawn due to crucial erros in equations (24)--(31).

Let $G$ be a simple, simply connected algebraic group over an algebraically closed field of positive characteristic $p$. In recent work, the authors have studied a graded analogue of the category of rational $G$-modules. These gradings are…

This paper has been withdrawn while the author verifies the literature.

In this text we signal a serious gap in the proof of the main theorem of our paper and explain which parts of the statement remain valid. In fact, the main theorem remains valid unless possibly the variety does not admit…

This paper has been withdrawn by the auther due to an error

The paper has been withdrawn.