local version - University of Arizona Math
... √ χf is the quadratic character of Gal(F /Fn ) associated to the extension Fn ( f )/Fn . This means that ...
... √ χf is the quadratic character of Gal(F /Fn ) associated to the extension Fn ( f )/Fn . This means that ...
![arXiv:0706.3441v1 [math.AG] 25 Jun 2007](http://s1.studyres.com/store/data/017784481_1-dd1160ad974ad834977ad61a663d12c3-300x300.png)
Toroidal deformations and the homotopy type of Berkovich spaces
... A non-Archimedean field is a field k endowed with an absolute value | · | : k× → R satisfying the ultrametric inequality: |a + b| É max{|a|, |b|}. We will always assume that (k, | · |) is complete. Morphisms are isometric. The closed unit ball k◦ = {a ∈ k, |a| É 1} is a local ring with fraction fiel ...
... A non-Archimedean field is a field k endowed with an absolute value | · | : k× → R satisfying the ultrametric inequality: |a + b| É max{|a|, |b|}. We will always assume that (k, | · |) is complete. Morphisms are isometric. The closed unit ball k◦ = {a ∈ k, |a| É 1} is a local ring with fraction fiel ...
Chapter I, Section 6
... with R Noetherian. X is Noetherian if it has a finite such covering [Liu, 2.3.45]. If X is locally Noetherian, then OX is coherent, a quasi-coherent sheaf of OX modules is coherent iff it is locally finitely generated, and every quasi-coherent subsheaf of a coherent sheaf of OX modules is coherent. ...
... with R Noetherian. X is Noetherian if it has a finite such covering [Liu, 2.3.45]. If X is locally Noetherian, then OX is coherent, a quasi-coherent sheaf of OX modules is coherent iff it is locally finitely generated, and every quasi-coherent subsheaf of a coherent sheaf of OX modules is coherent. ...