Morphisms of Varieties over Ample Fields
ثبت نشده
چکیده
We strengthen a result of Michiel Kosters by proving the following theorems: (*) Let φ: W → V be a finite surjective morphism of algebraic varieties over an ample field K. Suppose V has a simple K-rational point a such that a / ∈ φ(W (Kins)). Then, card(V (K)rφ(W (K)) = card(K). (**) Let K be an infinite field of positive characteristic and let f ∈ K[X] be a nonconstant monic polynomial. Suppose all zeros of f in K̃ belong to Kins rK. Then, card(K r f(K)) = card(K). MR Classification: 12E30 Directory: \Jarden\Diary\JBary 29 November 2017
منابع مشابه
MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM
We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.
متن کاملToroidalization of locally toroidal morphisms of 3-folds
A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.
متن کاملBirational Geometry and Localisation of Categories With Appendices
We explore connections between places of function fields over a base field F and birational morphisms between smooth F varieties. This is done by considering various categories of fractions involving function fields or varieties as objects, and constructing functors between these categories. The main result is that in the localised category S b Sm(F ), where Sm(F ) denotes the usual category of...
متن کاملBirational Geometry and Localisation of Categories
The basic theme of this paper is to explore connections between places of function fields over a base field F of characteristic zero and birational morphisms between smooth F -varieties. This is done by considering various localised categories involving function fields or varieties as objects, and constructing functors between these categories. The main result is that in the localised category ...
متن کاملCanonical Heights, Invariant Currents, and Dynamical Systems of Morphisms Associated with Line Bundles
We construct canonical heights of subvarieties for dynamical systems of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems over C. Introduction Let X be a projective variety over a field K and fi : X → X (i = 1, · · · , k) morphisms over K. Let L be a line bundle on X, and d > k a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017