Is there an example that étale morphism (of degree $d,d<\infty$) $\pi: X\rightarrow Y$, s.t. all its Deck transformations homotopic to $Id_X$,except the trivial one, where $Y$ is general Enriques surface over $\mathbb{C}$.
2026-03-29 22:07:39.1774822059
Étale morphism has all its Deck transformation homotopic to identity
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Any finite cover between two nonsingular elliptic curves would do the job.