Lubin-Tate extensions and Carlitz module over a projective line: an explicit connection

In this article we consider different approaches for constructing maximal abelian extensions local and global geometric fields. The Lubin–Tate theory plays key role in the extension construction case of fields, Drinfeld modules are particular interest. paper simpliest special projective line which is called Carlitz module. introduction, provide motivation a brief historical background on topics covered work. first second sections information about third section present two main results: • an explicit connection between field over finite field: it proved that tower module induces extensions. Artin maps function arbitrary smooth irreducible curve completions rings at closed points curve. last formulate open problems interesting directions further research, include generalization result consideration higher rank.