Exercise 7.3.16 (Arithmetic fracture square). Show that for every spectrum \(X\), the commutative squares
are pullback squares. In the first two squares, the products are taken over all prime numbers \(p\); the third square is asserted for every prime \(p\).
Hint: in each case, apply Lemma 7.3.14 to the fiber of the comparison map, taking \(P\) to be the set of all primes.
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