ScalingStacks

Subsection [04XF]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

(3.3) Let YY be a KK-analytic space, let BB be a topological space and let f:Y→Bf\colon Y\to B be a continuous map. Then we say that ff is an nn-dimensional affinoid torus fibration if we can cover BB by open subsets UU such that there exist an open subset VV of Nℝ≅ℝnN_{\mathbb{R}}\cong\mathbb{R}^{n} and a commutative diagram

f−1​(U)\textstyle{f^{-1}(U)\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}f\scriptstyle{f}ρT−1​(V)\textstyle{\rho_{T}^{-1}(V)\ignorespaces\ignorespaces\ignorespaces\ignorespaces}ρT\scriptstyle{\rho_{T}}U\textstyle{U\ignorespaces\ignorespaces\ignorespaces\ignorespaces}V\textstyle{V}

where the upper horizontal map is an isomorphism of KK-analytic spaces and the lower horizontal map is a homeomorphism.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.