Definition 72.17.1. Let k be a field. Let X be a proper algebraic over k. Let \mathcal{F} be a coherent \mathcal{O}_ X-module. In this situation the Euler characteristic of \mathcal{F} is the integer
\chi (X, \mathcal{F}) = \sum \nolimits _ i (-1)^ i \dim _ k H^ i(X, \mathcal{F}).
For justification of the formula see below.
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