EXPLICIT SURJECTIVITY RESULTS FOR DRINFELD MODULES OF RANK 2
- 주제(기타) Mathematics
- 설명문(일반) [Chen, Imin] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada; [Lee, Yoonjin] Ewha Womans Univ, Dept Math, 52 Ewhayeodae Gil, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 CAMBRIDGE UNIV PRESS
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000160092
- 본문언어 영어
- Published As http://dx.doi.org/10.1017/nmj.2017.26
초록/요약
Let K = F-q (T) and A = F-q [T]. Suppose that phi is a Drinfeld A module of rank 2 over K which does not have complex multiplication. We obtain an explicit upper bound (dependent on phi) on the degree of primes} of K such that the image of the Galois representation on the} - torsion points of phi is not surjective, in the case of q odd. Our results are a Drinfeld module analogue of Serre's explicit large image results for the Galois representations on p - torsion points of elliptic curves (Serre, Proprietes galoisiennes des points d'ordre fi ni des courbes elliptiques, Invent. Math. 15 (1972), 259{331; Serre, Quelques applications du theoreme de densite de Chebotarev, Inst. Hautes Etudes Sci. Publ. Math. 54 (1981), 323{401.) and are unconditional because the generalized Riemann hypothesis for function fi elds holds. An explicit isogeny theorem for Drinfeld A - modules of rank 2 over K is also proven.
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