Blar i forfatter "Quick, Gereon"

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    • Making the motivic group structure on the endomorphisms of the projective line explicit 

      Balch Barth, Viktor; Hornslien, William; Quick, Gereon; Wilson, Glen Matthew (Journal article; Tidsskriftartikkel; Peer reviewed, 2024-12-13)
      We construct a group structure on the set of pointed naive homotopy classes of scheme morphisms from the Jouanolou device to the projective line. The group operation is defined via matrix multiplication on generating sections of line bundles and only requires basic algebraic geometry. In particular, it is completely independent of the construction of the motivic homotopy category. We show that ...

    • Representability of the local motivic Brouwer degree 

      Quick, Gereon; Strand, Therese; Wilson, Glen Matthew (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-02-24)
      We study which quadratic forms are representable as the local degree of a map f:An→An with an isolated zero at 0 , following the work of Kass and Wickelgren who established the connection to the quadratic form of Eisenbud, Khimshiashvili, and Levine. Our main observation is that over some base fields k , not all quadratic forms are representable as a local degree. Empirically the local degree ...