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On the compactification of the Drinfeld modular curve of level Γ1Δ(n)
- Source :
- Journal of Number Theory. 232:75-100
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- Let p be a rational prime and q a power of p. Let n be a non-constant monic polynomial in F q [ t ] which has a prime factor of degree prime to q − 1 . In this paper, we define a Drinfeld modular curve Y 1 Δ ( n ) over A [ 1 / n ] and study the structure around cusps of its compactification X 1 Δ ( n ) , in a parallel way to Katz-Mazur's work on classical modular curves. Using them, we also define a Hodge bundle over X 1 Δ ( n ) such that Drinfeld modular forms of level Γ 1 ( n ) , weight k and some type are identified with global sections of its k-th tensor power.
Details
- ISSN :
- 0022314X
- Volume :
- 232
- Database :
- OpenAIRE
- Journal :
- Journal of Number Theory
- Accession number :
- edsair.doi...........951073db596bc122e3be177e54805f25