Grothendieck's Galois Theory

Postgraduate Thesis uoadl:3257522 4 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2023-01-19
Year:
2023
Author:
Tsantilas Theofilos
Supervisors info:
Εμμανουήλ Ιωάννης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Κοντογεώργης Αριστείδης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Συκιώτης Μιχαήλ, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Grothendieck's Galois Theory
Languages:
English
Translated title:
Θεωρία Galois κατά Grothendieck
Summary:
There are many Galois Theories throughout Mathematics. The
purpose of this dissertation is to intoduce the part of Grothendieck’s
Galois Theory for Schemes that is related to Artin’s Galois Theory of
finite field extensions; that is, Galois Theory of Finite Étale Algebras.
From early on, mathematicians had noticed the similarities the
Fundamental Theorem of Galois Theory and the Classification The-
orem of Covering Spaces share. Eventually, it was no other than
Grothendieck who understood their bond on a deeper level and
formulated a theory, Grothendieck’s Galois Theory for Schemes,
in which he succeeded to unify these two classification theorems.
Grothendieck’s theorem in its full generality classifies finite étale
coverings of a connected scheme using sets on which its étale funda-
mental group acts continuously. When seen from a field theoretic
point of view, the theorem classifies finite étale algebras of a field
using sets on which its absolute Galois group acts continuously. This
is the theorem we are pursuing.
Main subject category:
Science
Keywords:
Mathematics, Algebra, Galois Theory, Grothendieck, classification of field extensions, classification of covering spaces, etale algebras, etale, classification of etale algebras,classification of schemes, etale fundamental group
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
39
Number of pages:
151
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