arXiv Open Access 2020

An $\mathcal{O}$-acyclic variety of even index

John Christian Ottem Fumiaki Suzuki with an appendix by Olivier Wittenberg

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Abstrak

We give the first examples of $\mathcal{O}$-acyclic smooth projective geometrically connected varieties over the function field of a complex curve, whose index is not equal to one. More precisely, we construct a family of Enriques surfaces over $\mathbb{P}^{1}$ such that any multi-section has even degree over the base $\mathbb{P}^{1}$ and show moreover that we can find such a family defined over $\mathbb{Q}$. This answers affirmatively a question of Colliot-Thélène and Voisin. Furthermore, our construction provides counterexamples to: the failure of the Hasse principle accounted for by the reciprocity obstruction; the integral Hodge conjecture; and universality of Abel-Jacobi maps.

Topik & Kata Kunci

math.AG

Penulis (3)

John Christian Ottem

Fumiaki Suzuki

with an appendix by Olivier Wittenberg

Format Sitasi

APA MLA BibTeX

Ottem, J.C., Suzuki, F., Wittenberg, w.a.a.b.O. (2020). An $\mathcal{O}$-acyclic variety of even index. https://arxiv.org/abs/2010.06079

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓