Points of Small Height on Varieties Defined over a Function Field
نویسندگان
چکیده
منابع مشابه
Points of Small Height on Varieties Defined over a Function Field
We obtain a Bogomolov type of result for the additive group scheme in characteristic p. Our result is equivalent with a Bogomolov theorem for Drinfeld modules defined over a finite field.
متن کاملAlgebraic Points of Small Height Missing a Union of Varieties
Let K be a number field, Q, or the field of rational functions on a smooth projective curve over a perfect field, and let V be a subspace of KN , N ≥ 2. Let ZK be a union of varieties defined over K such that V * ZK . We prove the existence of a point of small height in V \ZK , providing an explicit upper bound on the height of such a point in terms of the height of V and the degree of a hypers...
متن کاملPoints of Bounded Height on Algebraic Varieties
Introduction 1 1. Heights on the projective space 3 1.1. Basic height function 3 1.2. Height function on the projective space 5 1.3. Behavior under maps 7 2. Heights on varieties 9 2.1. Divisors 9 2.2. Heights 13 3. Conjectures 19 3.1. Zeta functions and counting 19 3.2. Height zeta function 20 3.3. Results and methods 22 3.4. Examples 24 4. Compactifications of Semi-Simple Groups 26 4.1. A Con...
متن کاملCounting points on varieties over finite fields of small characteristic
We present a deterministic polynomial time algorithm for computing the zeta function of an arbitrary variety of fixed dimension over a finite field of small characteristic. One consequence of this result is an efficient method for computing the order of the group of rational points on the Jacobian of a smooth geometrically connected projective curve over a finite field of small characteristic. ...
متن کاملA Remark on Periodic Points on Varieties over a Field of Finite Type over Q
Let M be a field of finite type over Q and X a variety defined over M . We study when the set {P ∈ X(K) | f◦n(P ) = P for some n ≥ 1} is finite for any finite extension fields K of M and for any dominant K-morphisms f : X → X with deg f ≥ 2.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2009
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2009-026-0