Heights and drinfeld A-modules

To answer a question from Masser, Habegger proved that there are at most finitely many singular moduli that are algebraic units. In this thesis we prove an analogue result for Drinfeld 𝔽 𝑞[𝑡] -modules. That is, when 𝑞 is odd and 𝑞 > 5, there are at most finitely many singular moduli of Drinfeld 𝔽 𝑞[𝑡] - modules that are algebraic units. The proof applies techniques of heights. In particular, we study the variation of Taguchi heights and graded heights of Drinfeld 𝐴 -modules, and prove that the variation of Taguchi height can be linked to the variation of graded heights. Also, we obtain an analogue of Nakkajima and Taguchi’s result for the case of rank 2 CM Drinfeld 𝔽 𝑞[𝑡] -modules, as well as a lower bound of the Weil height of a singular modulus.