**DIPS 9/98**[tex source, PostScript, PDF file, dvi]-
**Title:**ON THE VINOGRADOV*C*-SPECTRAL SEQUENCE FOR DETERMINED SYSTEMS OF DIFFERENTIAL EQUATIONS**Author:**Dmitri GESSLERIn this paper a description of the term E

_{1}of the Vinogradov*C*-spectral sequence is given. Vanishing theorem for the group E_{1}^{p,n-1}, where n is a number of independent variables and p ³ 3, is proved for a system of evolution equations with a nondegenerate symbol. The group E_{1}^{2,n-1}for a scalar linear evolution equation with constant coefficients is computed.

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