Authors: Joseph KRASIL'SHCHIK, Alexander VERBOVETSKY
Lectures given in August 1998 at an advanced 5-day course in Levoca, Slovakia.
These lecture notes are a systematic and self-contained exposition of
the cohomological theories naturally related to partial differential
equations: the Vinogradov C- spectral sequence and the C-cohomology,
including the formulation in terms of the horizontal (characteristic)
cohomology. Applications to computing invariants of differential
equations are discussed. The lectures contain necessary introductory
material on the geometric theory of differential equations and
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