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Belyi's Theorems in Positive Characteristic.
- Source :
-
International Journal of Number Theory . Jul2020, Vol. 16 Issue 6, p1355-1368. 14p. 3 Diagrams. - Publication Year :
- 2020
-
Abstract
- There are two types of Belyi's Theorems for curves defined over finite fields of characteristic p , namely the Wild and the Tame p -Belyi Theorems. In this paper, we discuss them in the language of function fields. In particular, we provide a constructive proof for the existence of a pseudo-tame element introduced in [Y. Sugiyama and S. Yasuda, Belyi's theorem in characteristic two, Compos. Math. 156(2) (2020) 325–339], which leads to a self-contained proof for the Tame 2 -Belyi Theorem. Moreover, we provide unified and simple proofs for Belyi's Theorems unlike the known ones that use technical results from Algebraic Geometry. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRAIC geometry
*FINITE fields
*MATHEMATICS
*EVIDENCE
Subjects
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 16
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 144422717
- Full Text :
- https://doi.org/10.1142/S1793042120500712