magistrsko delo
Rok Havlas (Author), Primož Moravec (Mentor)

Abstract

Delo se ukvarja s perfektoidnimi prostori, razredom objektov v p-adični geometriji, ki jih je vpeljal fieldsov nagrajenec Peter Scholze leta 2011 v svoji doktorski disertaciji. Najprej si ogledamo nekaj osnov teorije valuacij in adičnih prostorov, ki predstavljajo geometrijsko ozadje teme. Nato definiramo perfektoidne kolobarje in polja in si ogledamo nekaj njihovih lastnosti. Vpeljemo funktor naklona, ki nam omogoča prehajanje med objekti v karakteristiki 0 in karakteristiki p. Za konec si še ogledamo perfektoidne prostore, ki so v grobem ravno skupaj zlepljene perfektoidne algebre, podobno kot so snopi ravno skupaj zlepljeni afini snopi.

Keywords

matematika;valuacija;Huberjev kolobar;adičen prostor;perfektoidi;naklonska ekvivalenca;perfektoidni prostor;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [R. Havlas]
UDC: 511
COBISS: 18902873 Link will open in a new window
Views: 1114
Downloads: 253
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Other data

Secondary language: English
Secondary title: Perfectoid spaces
Secondary abstract: The work is about perfectoid spaces, a class of objects in p-adic geometry that was introduced by the Fields medalist Peter Scholze in his PhD thesis in 2011. First, we will discuss some basic theory of valuations and adic spaces, which represent the geometric background of the topic. Then we define perfectoid rings and fields and look at their properties. We introduce the tilt functor, a tool that helps us to transfer from characteristic 0 to characteristic p. At the end, we look at perfectoid spaces, which we get by glueing together perfectoid algebras, similarly to how we get the schemes from affine schemes.
Secondary keywords: valuation;Huber ring;adic space;perfectoids;tilting equivalence;perfectoid space;
Type (COBISS): Master's thesis/paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 2. stopnja
Pages: IX, 66 str.
ID: 11399759