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memoria.pdf (435.23 KB)

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Bachelor thesis

Publication date

2018-06-27

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cc-by-nc-nd (c) Nil Garcés de Marcilla Escubedo, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/125803

The Quillen-Suslin theorem

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Abstract

[en] The Quillen-Suslin theorem is usually stated as "Let $P$ be a finitely generated projective module over $k [ x_{1},...,x_{n}]$ . Then P is free". Before being proven independently and in its full generality by Quillen and Suslin in 1976, this question was usually referred to as the "Serre’s Conjecture", and stood as one of the most relevant open problems in algebra and affine algebraic geometry for twenty years. In this memoir we provide in detail all the algebraic tools needed to have a good understanding of the basic mathematics surrounding this theorem and its more elementary proof by Vaserstein, as well as some algorithms related to it.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Carlos D'Andrea

Subject

Mòduls projectius (Àlgebra), Treballs de fi de grau, Àlgebra commutativa, Algorismes computacionals

Subject (English)

Commutative algebra, Bachelor's theses, Computer algorithms, Projective modules (Algebra)

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

GARCÉS DE MARCILLA ESCUBEDO, Nil. The Quillen-Suslin theorem. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/125803

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