Abstract: We study the arithmetic of supersingular Drinfeld modules, with an emphasis on rank-3 Drinfeld modules over finite fields. We discuss how generalized j-invariants classify isomorphism classes and describe explicit constructions of supersingular examples. We then investigate stabilization formulas for spaces of bounded-degree morphisms between supersingular Drinfeld modules, extending known results from rank 2 to higher-rank cases through explicit computations and examples. In particular, we present evidence for linear growth formulas governing the dimensions of these morphism spaces in rank 3. Finally, we explain how endomorphism rings of supersingular Drinfeld modules can be used to construct semifield codes and Maximum Rank Distance (MRD) codes, highlighting new connections between Drinfeld modules and coding theory.

 

Organizer: Fu-Tsun Wei (NTHU)