Related papers: Geometric Auslander criterion for flatness

The paper has been withdrawn

This paper was withdrawn by the author due to an error in the proof of the main result; essentially the parameter R used in the proof may depend on the manifold (M, g), not just on dimension and pinching constant.

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

We prove that, if F is a coherent sheaf of modules over the source of a morphism f:X->Y of complex-analytic spaces, where Y is smooth, then the stalk of F at a point x in X is flat over R, the local ring of the target at f(x) if and only if…

withdrawn by the authors because of an error.

The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

withdrawed due to a substantial error.

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

This paper is withdrawn.

Paper withdrawn. The argument was based on a misconception

This paper has been withdrawn by the author due to an error.

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.

The paper has been withdrawn by the author due an error in the proof of Theorem 3.2.

Paper withdrawn by authors. See new version in this same listing.

This paper has been withdrawn by the authors due to an error in the main theorem.

This paper has been withdrawn by the author, due a critical mistake on page 3.

This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.

This paper has been withdrawn by the author due to an error in the proof.