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On field extensions given by periods of Drinfeld modules
- Publication Year :
- 2019
-
Abstract
- In this short note, we answer a question raised by M. Papikian on a universal upper bound for the degree of the extension of $K_\infty$ given by adjoining the periods of a Drinfeld module of rank 2. We show that contrary to the rank 1 case such a universal upper bound does not exist, and the proof generalises to higher rank. Moreover, we give an upper and lower bound for the extension degree depending on the valuations of the defining coefficients of the Drinfeld module. In particular, the lower bound shows the non-existence of a universal upper bound.<br />7 pages; v1->v2: corrected typos, added/changed references, now 8 pages
- Subjects :
- Rank (linear algebra)
Degree (graph theory)
Mathematics - Number Theory
General Mathematics
010102 general mathematics
Extension (predicate logic)
01 natural sciences
Upper and lower bounds
Combinatorics
Field extension
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
Drinfeld module
Number Theory (math.NT)
0101 mathematics
Mathematics
11G09
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....bd6ddcc00757510259c7adc47c35ce5e