arXiv Open Access 2020

Relative internality and definable fibrations

Rémi Jaoui Léo Jimenez Anand Pillay

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Abstrak

We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collapse of the groupoid in an earlier work of the second author), and relating it to orthogonality, triviality of fibrations, the strong canonical base property, differential Galois theory, and GAGA. We prove that $\mathrm{DCF}_0$ does not have the strong canonical base property, correcting an earlier proof. We also prove that the theory $\mathrm{CCM}$ of compact complex manifolds does not have the strong CBP, and initiate a study of the definable Galois theory of projective bundles. In the rest of the paper we study definable fibrations in $\mathrm{DCF}_0$, where the general fibre is internal to the constants, including differential tangent bundles, and geometric linearizations. We obtain new examples of higher rank types orthogonal to the constants.

Topik & Kata Kunci

math.LO

Penulis (3)

Rémi Jaoui

Léo Jimenez

Anand Pillay

Format Sitasi

APA MLA BibTeX

Jaoui, R., Jimenez, L., Pillay, A. (2020). Relative internality and definable fibrations. https://arxiv.org/abs/2009.06014

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Informasi Jurnal

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