On the compactification of the Drinfeld modular curve of level [formula omitted

Abstract

Let p be a rational prime and q a power of p. Let n be a non-constant monic polynomial in Fq[t] which has a prime factor of degree prime to q−1. In this paper, we define a Drinfeld modular curve Y1Δ(n) over A[1/n] and study the structure around cusps of its compactification X1Δ(n), in a parallel way to Katz-Mazur's work on classical modular curves. Using them, we also define a Hodge bundle over X1Δ(n) such that Drinfeld modular forms of level Γ1(n), weight k and some type are identified with global sections of its k-th tensor power.