Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Chatzidavari Stavroula
Supervisors info:
Κοντογεώργης Αριστείδης, Kαθηγητής, Τμήμα μαθηματικών , Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνων
Original Title:
Εισαγωγή στα Drinfeld Modules
Translated title:
Introduction to Drinfeld Modules
Summary:
The ring of integers Z, has many common properties with k[x] the ring of polynomials over a finite field therefore it is natural to expect that there will be parallels in K[x] for many of the results we can prove for Z.
In this paper we will study the technique of Drinfeld Modules in relation with class field theory.In order to define what a Drinfeld Module is we will first present additive polynomials and some basic results from non-Archimedean analysis. We will also define the Carlitz module using a function analogous to the exponential function. Then, we will demonstrate a series of analogues in order to compare the Cyclotomic number fields with Cyclotomic function fields. Finally we will describe the function field equivalent for the Kronecher-Weber theorem.
Main subject category:
Science
Keywords:
Drinfeld modules, function fields, cyclotomic field, mom-Archimedean analysis, algebraic number theory
