Artin's Vanishing Theorem is a fundamental result in algebraic geometry that deals with the cohomology of coherent sheaves. It states that under certain conditions, the higher cohomology groups of a coherent sheaf vanish on proper schemes, meaning they can be computed in terms of the sheaf's global sections. This theorem highlights the deep relationship between sheaves and their cohomological properties, establishing key results about the behavior of sections of sheaves over various types of spaces.
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