Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Αριστείδης Κοντογεώργης, Αναπληρωτής καθηγητής, τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό πανεπιστημίο Αθηνών
Μιχάλης Μαλιάκας, Καθηγητής, τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό πανεπιστημίο Αθηνών
Ιωάννης Εμμανουήλ, Επίκουρος καθηγητής, τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό πανεπιστημίο Αθηνών
Original Title:
Λ-δακτύλιοι και το σώμα με ένα στοιχείο
Translated title:
lambda-rings and the field with one element
Summary:
In the current thesis we study the lambda rings as Grothendieck defined them. We explore how we can enstablish a theory about the elucive field with one element based on the theory of lambda rings. We will define the algebras over the field with one element and as a result we will have a canditate about the algebraic object which we will define as field with one element.
We continue by defining the extentions of the field with one element and then we define an antiequivalence between the category of particular family of algebras over the field with one element and finite sets with an continues action of a certain monoid In correspondence with classical Galois theory of etale finite algebras over some field.
In the last chapter we define the lambda spectrum of an algebra over the field with one element, and identify each spectrum of a commutative ring with a specific subset of the lambda spectrum of an algebra over the field with one element. Lats but ont least we explore how Smirnov's proposals emerge from this theory about the field with one element via lambda rings.
Main subject category:
Science
Other subject categories:
Mathematics
Keywords:
Galois, Smirnov, Borger, 'etale
