Geometric class field theory is an analog of the classical class field theory over function fields in which functions are replaced by sheaves. In the first part of my talk, I will formulate the result and explain its proof over C (the field of complex numbers).  

In the  second part of the talk, I will try to outline the proof in the case of finite fields and indicate how this result implies the classical unramified global class field theory over function fields. 

Most of the talk will be independent of the first one. 

References: https://arxiv.org/pdf/1507.00104.pdf, https://dspace.library.uu.nl/handle/1874/206061 

Key words: Abel-Jacobi map, l-adic sheaves, sheaf-function correspondence.