Essays about: "Algebraic Geometry"

Showing result 1 - 5 of 18 essays containing the words Algebraic Geometry.

  1. 1. Elementary proof of the Riemann—Roch Theorem

    University essay from Uppsala universitet/Algebra, logik och representationsteori

    Author : Hampus Sundgren; [2023]
    Keywords : Algebraic Geometry; Riemann–Roch; The Riemann–Roch Theorem; Divisors; Differentials; L D ; l D ; Vector space L D ; Proof of the Riemann–Roch Theorem;

    Abstract : This thesis will cover an elementary proof of the Riemann–Roch Theorem for planecurves. We will introduce the notions of divisors, which is a convenient way of com-puting multiplicities of rational function, then continuing by introducing differentials. READ MORE

  3. 2. Octonion Algebras over Schemes and the Equivalence of Isotopes and Isometric Quadratic Forms

    University essay from Uppsala universitet/Matematiska institutionen

    Author : Victor Hildebrandsson; [2023]
    Keywords : Algebraic geometry; octonion algebras;

    Abstract : Octonion algebras are certain algebras with a multiplicative quadratic form. In 2019, Alsaody and Gille showed that, for octonion algebras over unital commutative rings, there is an equivalence between isotopes and isometric quadratic forms. READ MORE

  4. 3. Braids and configuration spaces

    University essay from Uppsala universitet/Geometri och fysik

    Author : Andersson Rasmus; [2023]
    Keywords : braids; braid groups; configuration space; algebraic topology; group theory; fundamental group; covering spaces;

    Abstract : A configuration space is a space whose points represent the possible states of a given physical system. As such they appear naturally both in theoretical physics and technical applications. READ MORE

  5. 4. Profinite groups

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Juan Moreno Poncela; [2023]
    Keywords : Profinite Groups; Infinite Galois Theory; Mathematics and Statistics;

    Abstract : This thesis provides a comprehensive study of profinite groups, which are fascinating mathematical objects that have attracted significant interest in modern algebraic research. Profinite groups are infinite generalizations of finite groups and share many similarities with them. READ MORE

  6. 5. On Noetherian Rings

    University essay from Örebro universitet/Institutionen för naturvetenskap och teknik

    Author : Kevin Miramadi; [2023]
    Keywords : ;

    Abstract : In this thesis we study a special class of rings called Noetherian rings. Theserings satisfy certain finite conditions on their ideals and appear in manydifferent fields of algebra. READ MORE