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JOURNALS // Chebyshevskii Sbornik // Archive

Chebyshevskii Sb., 2021 Volume 22, Issue 2, Pages 90–103 (Mi cheb1024)

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

N. V. Elizarov, S. V. Vostokov

Saint Petersburg State University (St. Petersburg)

Abstract: In this article we consider different approaches for constructing maximal abelian extensions for local and global geometric fields. The Lubin–Tate theory plays key role in the maximal abelian extension construction for local geometric fields. In the case of global geometric fields, Drinfeld modules are of particular interest. In this paper we consider the simpliest special case of Drinfeld modules for projective line which is called the Carlitz module.
In the introduction, we provide motivation and a brief historical background on the topics covered in the work.
In the first and second sections we provide brief information about Lubin–Tate modules and Carlitz module.
In the third section we present two main results:

In the last section we formulate different open problems and interesting directions for further research, which include generalization first result for an arbitrary smooth projective curve over a finite field and consideration Drinfeld modules of higher rank.

Keywords: class field theory, Lubin–Tate theory, Carlitz module, Drinfeld modules, Artin map, maximal abelian extension, projective line over a finite field.

UDC: 51

Language: English

DOI: 10.22405/2226-8383-2018-22-2-90-103



© Steklov Math. Inst. of RAS, 2025