Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Αριστείδης Κοντογεώργης, Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών
Original Title:
Το αντίστροφο πρόβλημα της θεωρίας Galois
Translated title:
The inverse problem of Galois theory
Summary:
The Inverse Galois problem is a central problem in algebra. In its classical form, it concerns the classification of the finite groups that occur as Galois groups of polynomials with rational coefficients but the problem has been studied in the context of many fields. In this thesis, we present techniques and results about the problem such as Hilbert's Irreducibility Theorem, the correspondence between Riemann surfaces and algebraic extensions of the field of rational functions with complex coefficients and the Rigidity Criteria.
Main subject category:
Science
Keywords:
inverse Galois problem, rigidity criteria, Riemann's existence theorem
