论文标题
相对内在和可确定的纤维
Relative internality and definable fibrations
论文作者
论文摘要
我们首先阐述了稳定理论中相对内在的相对内在理论，重点是统一相对内在的概念（在第二作者的早期作品中称为群体胶体的崩溃），并将其与正交性，纤维化，强大的规范基础特性，差异化的galois理论和加加（Gaga）联系起来。 我们证明$ \ mathrm {dcf} _0 $没有强大的规范基本属性，可以纠正较早的证明。我们还证明，紧凑型复杂歧管的理论$ \ mathrm {ccm} $没有强大的CBP，并启动了对投射捆绑包的可定义的Galois理论的研究。在本文的其余部分中，我们研究了$ \ mathrm {dcf} _0 $中的可定义纤维，其中一般光纤是常数内部的，包括差分切线束和几何线性化。我们获得了与常数正交的高级类型的新示例。
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.
