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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.14876 |
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Table of Contents:
- We construct a surface over $\overline{\mathbb{F}}_p$ with $π_1^{ét}(X) = 1$ that is supersingular -- in the sense that $H^2_{ét}(X, \mathbb{Q}_{\ell}(1))$ is spanned by algebraic cycles -- but is not unirational. This provides a counterexample to a 1977 conjecture of Shioda. To achieve this, we produce new obstructions to unirationality for product-quotient surfaces.