A finiteness theorem for canonical heights attached to rational maps over function fields
نویسندگان
چکیده
منابع مشابه
A Finiteness Theorem for Canonical Heights Attached to Rational Maps over Function Fields
Let K be a function field, let φ ∈ K(T ) be a rational map of degree d ≥ 2 defined over K, and suppose that φ is not isotrivial. In this paper, we show that a point P ∈ P(K̄) has φ-canonical height zero if and only if P is preperiodic for φ. This answers affirmatively a question of Szpiro and Tucker, and generalizes a recent result of Benedetto from polynomials to rational functions. We actually...
متن کاملA FINITENESS THEOREM FOR ZERO-CYCLES OVER p-ADIC FIELDS
Contents Introduction 2 1. Homology theory and cycle map 6 2. Kato homology 12 3. Vanishing theorem 16 4. Bertini theorem over a discrete valuation ring 20 5. Surjectivity of cycle map 23 6. Blow-up formula 25 7. A moving lemma 28 8. Proof of main theorem 30 9. Applications of main theorem 33 Appendix A.
متن کاملA combinatorial model for reversible rational maps over finite fields
We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e. map-independent) distribution function R(x) = 1 − e−x(1 + x) has been conjectured to exist, for the normalized cycle lengths of the reduced map in the large fie...
متن کاملFINITENESS THEOREM ON ZERO-CYCLES OVER p-ADIC FIELDS
Contents Introduction 2 1. Homology theory and cycle map 6 2. Kato homology 11 3. Vanishing theorem 15 4. Bertini theorem over a discrete valuation ring 19 5. Surjectivity of cycle map 22 6. Blowup formula 24 7. A moving lemma 26 8. Proof of main theorem 28 9. Applications of main theorem 31 Appendix A. Resolution of singularities for embedded curves 34 References 39
متن کاملFiniteness theorems for algebraic groups over function fields
We prove the finiteness of class numbers and Tate-Shafarevich sets for all affine group schemes of finite type over global function fields, as well as the finiteness of Tamagawa numbers and Godement’s compactness criterion (and a local analogue) for all such groups that are smooth and connected. This builds on the known cases of solvable and semisimple groups via systematic use of the recently ...
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: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2009
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2009.008