Proposition 45.14.17 (0FIU)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 45: Weil Cohomology Theories
Section 45.14: Weil cohomology theories, III
Proposition 45.14.17 (cite)

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Proposition 45.14.17. Assume given data (D0), (D1), and (D2') satisfying axioms (A1) – (A8). Then we have a Weil cohomology theory.

Proof. We have axioms (A), (B) and (C)(a), (C)(c), and (C)(d) of Section 45.9 by Lemmas 45.14.5, 45.14.7, and 45.14.8. We have axiom (C)(b) by Lemma 45.14.16. Finally, the additional condition of Definition 45.11.4 holds because it is the same as our axiom (A8). $\square$

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