Original title: Serreho hypotéza o projektivních modulech nad okruhy polynomů
Translated title: Serre's conjecture on projective modules over polynomial rings
Authors: Young, Edward ; Shaul, Liran (advisor) ; Bird, Isaac (referee)
Document type: Bachelor's theses
Year: 2023
Language: eng
Abstract: This is an expository paper on the Quillen-Suslin Theorem, formerly known as Serre's Conjecture. A self-contained proof of this theorem is presented, followed by a discussion of the related Bass-Quillen Conjecture. The first chapter establishes the necessary theory, building on undergraduate algebra with the essentials of free, projective, and flat modules. The second chapter presents a complete proof of the theorem, dealing with regular rings, stably-free modules, and the related calculus of unimodular rows. The third and final chapter lists partial results surrounding the as yet unresolved Bass-Quillen Conjecture, offering brief explanations and suggestions for further reading. 1
Keywords: projective|module|commutative algebra|tensor product|polynomial ring; projektivní|modul|komutativní algebra|tenzor|okruhy polynomů

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/182987

Permalink: http://www.nusl.cz/ntk/nusl-532448


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses