学术报告（胡创强 2024.9.11)

摘要： The primary objective of this talk is to derive some results for rank one and rank two Drinfeld modules.  Drinfeld module is the main tool in the study of class field theory.  The definition field of $A$-Drinfeld module gives rise to the Hilbert class field of A. We demonstrate that the period lattice of the exponential functions corresponding to both modules behaves similarly to the period lattice of Carlitz modules, the standard Drinfeld modules defined over rational function field. Moreover, we employ Anderson’s t-motive to obtain the complete family of rank two Drinfeld modules.  Building upon the concepts introduced by van der Heiden, particularly with regard to rank two Drinfeld modules, we are able to reformulate the Weil pairing of Drinfeld modules of any rank using a specialized polynomial in multiple variables known as the Weil operator.