Marques Sophie

@math.sun.ac.za

Associate professor at Department of Mathematical Sciences, Stellenbosch University
Stellenbosch University

Marques Sophie


                     Download Compact PDF  
https://researchid.co/smarques
Sophie Marques is an Associate Professor of Mathematics at Stellenbosch University in South Africa. Her research lies at the intersection of algebraic geometry, number theory, and algebra, with contributions ranging from ramification theory and group schemes to invariant theory, near-vector spaces, and categorical structures.
She earned her PhD with honors in Algebraic Geometry in 2013, jointly from the University of Bordeaux I and the Università degli Studi di Padova, under the supervision of Boas Erez and Marco Garuti. Before that, she completed her Master’s in Pure Mathematics at Bordeaux and ranked among the national laureates of the Agrégation in Mathematics. Her early academic path began with a Bachelor’s in Mathematics and Computer Science at the Université de Pau et des Pays de l’Adour, where she graduated first in her class.
Before joining Stellenbosch, Sophie held postdoctoral positions at the University of Cape Town and at the Courant Institute of Mathematical Sciences in N

EDUCATION

Bordeaux I and the Università degli Studi di Padova, under the supervision of Boas Erez and Marco Garuti. My Master’s in Pure Mathematics (2007–2010, Bordeaux I) included thesis work with Anna Cadoret and Laurent Herr. In 2009, I was awarded the Agrégation in Mathematics. I previously earned a Bachelor’s in Mathematics and Computer Science (2004–2007, Université de Pau et des Pays de l’Adour, first of class) and an Internet and Computing Certificate (2007). More recently, I completed the Online CREST Training Course for Supervisors of Doctoral Candidates at African Universities (2020, with distinction).

RESEARCH, TEACHING, or OTHER INTERESTS

Algebra and Number Theory, Geometry and Topology, Discrete Mathematics and Combinatorics, General Mathematics
17

Scopus Publications

110

Scholar Citations

6

Scholar h-index

4

Scholar i10-index

Scopus Publications

  • Distributive decomposition of near-vector spaces
    Leandro Boonzaaier, Sophie Marques, Daniella Moore
    Journal of Algebra and Its Applications, 2026
    This paper characterizes the regularity of arbitrary near-vector spaces by representing them as direct sums of vector spaces over division rings formed by distributive elements. This approach allows us to define the dimension of a near-vector space in terms of the dimensions of these summands, providing new insights into the structure and properties of near-vector spaces.
  • Galois descent theorem in general categories
    Sophie Marques
    Research in Mathematical Sciences, 2026
    The theory of descent, originating from the work of Évariste Galois and further developed by mathematicians such as Weil, Grothendieck, and Janelidze, has become a fundamental tool in algebraic geometry and category theory. This paper presents a new categorical framework for Galois descent and establishes a Galois descent theorem.
  • Why is the Category of Near-Vector Spaces Abelian?
    Zurab Janelidze, Sophie Marques, Daniella Moore
    Applied Categorical Structures, 2026
  • Near-linear algebra
    Sophie Marques, Daniella Moore
    Journal of Algebra and Its Applications, 2025
    In this paper, we demonstrate that the realm of near-vector spaces enables us to address nonlinear problems while also providing access to most of the tools that linear algebra offers. We establish fundamental results for near-vector spaces, which serve to extend classical linear algebra into the realm of near-linear algebra. Within this paper, we finalize the algebraic proof that for a given scalar group [Formula: see text], any nonempty [Formula: see text]-subspace that remains stable under addition and scalar multiplication constitutes an [Formula: see text]-subspace. We prove that any quotient of a near-vector space by an [Formula: see text]-subspace is itself a near-vector space, along with presenting the First Isomorphism Theorem for near-vector spaces. In doing so, we obtain comprehensive descriptions of the span. By defining linear independence outside the quasi-kernel, we introduce a new concept of basis. We also establish that near-vector spaces are characterized based on the presence of a scalar basis.
  • A note on the transport of (near-)field structures
    Leandro Boonzaaier, Sophie Marques
    Afrika Matematika, 2025
    This paper addresses the question: given a scalar group, can we determine all the additions that transform this scalar group into a (near-)field? A key approach to addressing this problem involves transporting (near-)field structures via multiplicative automorphisms. We compute the set of continuous multiplicative automorphisms of the real and complex fields and analyze their structures. Additionally, we characterize the endo-bijections on the scalar group that define these additions.
  • A characterization of ramification groups via jet algebras
    Sophie Marques, Luigi Pagano
    European Journal of Mathematics, 2024
    We present a functorial method to define ramification groups, identifying them as inertia groups of an induced action on composite jet algebras. This framework lays the foundation for defining higher ramification groups for actions involving group schemes. To achieve this, we introduce Taylor maps within the category of commutative unitary rings at prime ideals of an $$R$$ R -algebra and compute their kernels for algebras of finite type over a field with separably generated residue fields.
  • Toward an intuitive understanding of the structure of near-vector spaces
    K.-T. Howell, S. Marques
    Communications in Algebra, 2022
  • The geometry of the moduli space of non-cyclic biquadratic field extensions
    Mpendulo Cele, Sophie Marques
    Quaestiones Mathematicae, 2022
  • Cubic function fields with prescribed ramification
    Valentijn Karemaker, Sophie Marques, Jeroen Sijsling
    International Journal of Number Theory, 2021
    This paper describes cubic function fields [Formula: see text] with prescribed ramification, where [Formula: see text] is a rational function field. We give general equations for such extensions, an explicit procedure to obtain a defining equation when the purely cubic closure [Formula: see text] of [Formula: see text] is of genus zero, and a description of the twists of [Formula: see text] up to isomorphism over [Formula: see text]. For cubic function fields of genus at most one, we also describe the twists and isomorphism classes obtained when one allows Möbius transformations on [Formula: see text]. The paper concludes by studying the more general case of covers of elliptic and hyperelliptic curves that are ramified above exactly one point.
  • A complete study of the ramification for any separable cubic global function field
    Sophie Marques, Jacob Ward
    Research in Number Theory, 2019
  • An explicit triangular integral basis for any separable cubic extension of a function field
    Sophie Marques, Kenneth Ward
    European Journal of Mathematics, 2019
  • Cubic fields: a primer
    Sophie Marques, Kenneth Ward
    European Journal of Mathematics, 2019
  • Holomorphic differentials of certain solvable covers of the projective line over a perfect field
    Sophie Marques, Kenneth Ward
    Mathematische Nachrichten, 2018
  • Generic polynomials for cyclic function field extensions over certain finite fields
    Sophie Marques
    European Journal of Mathematics, 2018
  • When are permutation invariants cohen–Macaulay over all fields?
    Ben Blum-Smith, Sophie Marques
    Algebra and Number Theory, 2018
  • Existence of slices on a tame context
    Sophie Marques
    European Journal of Mathematics, 2015
  • Tame actions of affine group schemes and tame stacks
    Sophie Marques
    Comptes Rendus Mathematique, 2012

RECENT SCHOLAR PUBLICATIONS

  • Distributive decomposition of near-vector spaces
    L Boonzaaier, S Marques, D Moore
    Journal of Algebra and Its Applications 25 (09), 2650088 , 2026
    2026
    Citations: 4
  • Galois descent theorem in general categories
    S Marques
    Research in the Mathematical Sciences 13 (2), 49 , 2026
    2026
  • Automorphism groups of direct products of multiplicative monoids of certain rings
    J Atalaye, L Baker, S Marques
    arXiv preprint arXiv:2605.06119 , 2026
    2026
  • Why is the category of near-vector spaces abelian?
    Z Janelidze, S Marques, D Moore
    Applied Categorical Structures 34 (1), 3 , 2026
    2026
    Citations: 2
  • Inner products for strongly regular near-vector spaces and duality for finite dimensional near-vector spaces
    L Boonzaaier, S Marques, D Moore
    arXiv preprint arXiv:2511.11774 , 2025
    2025
  • Comparing the face rings of a boolean complex and its barycentric subdivision
    B Blum-Smith, S Marques
    arXiv preprint arXiv:2507.20037 , 2025
    2025
  • A note on gluing: a pillar of algebraic geometry
    S Marques, D Mgani
    arXiv preprint arXiv:2505.02264 , 2025
    2025
  • A note on the moduli spaces of free algebras of rank 2
    S Marques
    arXiv preprint arXiv:2504.16241 , 2025
    2025
  • Near-linear algebra
    S Marques, D Moore
    Journal of Algebra and Its Applications 24 (05), 2550125 , 2025
    2025
    Citations: 8
  • Multiplicative near-vector spaces
    L Boonzaaier, S Marques, D Moore
    arXiv preprint arXiv:2504.03288 , 2025
    2025
    Citations: 2
  • A note on the transport of (near-) field structures
    L Boonzaaier, S Marques
    Afrika Matematika 36 (1), 57 , 2025
    2025
    Citations: 4
  • A study of a recursive sequence of polynomials revealing weighted Catalan Numbers
    S Marques, E Mrema
    arXiv preprint arXiv:2501.13693 , 2025
    2025
  • A characterization of ramification groups via jet algebras
    S Marques, L Pagano
    European Journal of Mathematics 10 (4), 67 , 2024
    2024
    Citations: 1
  • On the automorphism group of the monoid of the integers modulo a prime power
    J Atalaye, L Baker, S Marques
    arXiv preprint arXiv:2408.06278 , 2024
    2024
    Citations: 1
  • A characterization of ramification groups via Taylor morphism
    S Marques, L Pagano
    arXiv preprint arXiv:2402.05836 , 2024
    2024
  • A Categorical Perspective on Gluing
    S Marques, D Mgani
    arXiv preprint arXiv:2401.10117 , 2024
    2024
    Citations: 1
  • When is a 2-Power Cyclotomic Extension cyclic?
    S Marques, E Mrema
    arXiv preprint arXiv:2308.08865 , 2023
    2023
    Citations: 1
  • 2-Cyclotomic field extensions
    S MARQUES, E MREMA
    arXiv preprint arXiv:2308.08865 , 2023
    2023
    Citations: 1
  • Gluing Data categories and gluing data functors
    S Marques, D Mgani
    arXiv preprint arXiv:2304.14093 , 2023
    2023
  • Near-field structures on a given scalar group
    S Marques, L Boonzaaier
    arXiv preprint arXiv:2211.09877 , 2022
    2022

MOST CITED SCHOLAR PUBLICATIONS

  • Toward an intuitive understanding of the structure of near-vector spaces
    KT Howell, S Marques
    Communications in Algebra 50 (9), 3664-3677 , 2022
    2022
    Citations: 13
  • When are permutation invariants Cohen–Macaulay over all fields?
    B Blum-Smith, S Marques
    Algebra & Number Theory 12 (7), 1787-1821 , 2018
    2018
    Citations: 13
  • Cubic fields: A primer
    S Marques, K Ward
    European Journal of Mathematics 5 (2), 551-570 , 2019
    2019
    Citations: 12
  • Holomorphic differentials of certain solvable covers of the projective line over a perfect field
    S Marques, K Ward
    Mathematische Nachrichten 291 (13), 2057-2083 , 2018
    2018
    Citations: 12
  • Near-linear algebra
    S Marques, D Moore
    Journal of Algebra and Its Applications 24 (05), 2550125 , 2025
    2025
    Citations: 8
  • A complete classification of cubic function fields over any finite field
    S Marques, K Ward
    arXiv preprint arXiv:1612.03534 , 2016
    2016
    Citations: 7
  • Distributive decomposition of near-vector spaces
    L Boonzaaier, S Marques, D Moore
    Journal of Algebra and Its Applications 25 (09), 2650088 , 2026
    2026
    Citations: 4
  • A note on the transport of (near-) field structures
    L Boonzaaier, S Marques
    Afrika Matematika 36 (1), 57 , 2025
    2025
    Citations: 4
  • Cubic function fields with prescribed ramification
    V Karemaker, S Marques, J Sijsling
    International Journal of Number Theory 17 (09), 2019-2053 , 2021
    2021
    Citations: 4
  • An explicit triangular integral basis for any separable cubic extension of a function field
    S Marques, K Ward
    European Journal of Mathematics 5 (4), 1252-1266 , 2019
    2019
    Citations: 4
  • Existence of slices on a tame context
    S Marques
    European Journal of Mathematics 1 (1), 54-77 , 2015
    2015
    Citations: 4
  • A complete study of the ramification for any separable cubic global function field
    S Marques, J Ward
    Research in Number Theory 5 (4), 36 , 2019
    2019
    Citations: 3
  • Generic polynomials for cyclic function field extensions over certain finite fields
    S Marques
    European Journal of Mathematics 4 (2), 585-602 , 2018
    2018
    Citations: 3
  • Actions modérées de schémas en groupes affines et champs modérés
    S Marques
    Comptes Rendus Mathematique 350 (3-4), 125-128 , 2012
    2012
    Citations: 3
  • Why is the category of near-vector spaces abelian?
    Z Janelidze, S Marques, D Moore
    Applied Categorical Structures 34 (1), 3 , 2026
    2026
    Citations: 2
  • Multiplicative near-vector spaces
    L Boonzaaier, S Marques, D Moore
    arXiv preprint arXiv:2504.03288 , 2025
    2025
    Citations: 2
  • The geometry of the moduli Space of non-cyclic biquadratic field extensions
    M Cele, S Marques
    Quaestiones Mathematicae 45 (10), 1501-1527 , 2022
    2022
    Citations: 2
  • Holomorphic differentials of solvable Galois towers of curves over a perfect field
    S Marques, K Ward
    arXiv preprint arXiv:1507.07023 , 2015
    2015
    Citations: 2
  • A characterization of ramification groups via jet algebras
    S Marques, L Pagano
    European Journal of Mathematics 10 (4), 67 , 2024
    2024
    Citations: 1
  • On the automorphism group of the monoid of the integers modulo a prime power
    J Atalaye, L Baker, S Marques
    arXiv preprint arXiv:2408.06278 , 2024
    2024
    Citations: 1