## Proof “ A la Grothendieck” [closed]

Grothendieck's proof of the well-known Ax–Grothendieck Theorem uses the elegant argument that the existence of a counterexample for the field $\mathbb C$ imply the existence of a counterexample for a finite field. Roughly speaking, we transfer the problem from $\mathbb C$ to finite fields.

recently, Will Sawin, here in mathoverflow, proved that the ring of Hamilton quaternions over $\mathbb H_{2^s}$ is reversible proving that the existence of a counterexample fore some $s$ imply the existence of a counterexample for $s=1$ or $s=2$, (a finite problem tha is solved with a computer).

There are other examples of this type of proof?

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Too vague and thus too broad. Vote to close. (BTW, please use CW mode when asking for a list of answers; there is a box to tick, you can still do this by editing the question.) – quid Jul 8 at 15:00
Maybe you can look at here: college-de-france.fr/media/historique/… – Mahdi Majidi-Zolbanin Jul 8 at 15:16