Deuring's Theory for Supersingular Drinfeld Modules

Student: Qureshi Ahmad

Supervisor: Satoshi Kondo

Educational Programme: Mathematics (Master)

Year of Graduation: 2017

This article describes an analogue of Deuring's theory for supersingular elliptic curves in the setting of supersingular Drinfeld modules. We first introduce all the terminology and definitions required to define Drinfeld modules. After they have been defined, we study morphisms between them and prove certain theorems about their homomorphism and endomorphism rings. All this leads up to the main result of this thesis which is a generalisation of (the main part of) Proposition 5.1 in [KY]. The latter deals with supersingular Drinfeld modules of rank 2. We generalise this to the case of arbitrary rank. Results from algebra will be assumed freely but, in the most non-trivial cases, references to the relevant literature will be provided.

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