Division algebras that ramify only on a plane quartic curve with simply connected components
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چکیده
Let k be an algebraically closed field of characteristic zero. Denote the projective plane over k by P2 = Proj k[x, y, z]. Let K be the field of rational functions on P2. We view K as the set of all rational functions of the form f/g ∈ k(x, y, z) where f and g are homogeneous forms in k[x, y, z] of the same degree. Since k is algebraically closed, the Brauer group of P2, denoted B(P2), is trivial [5, Proposition 10.5]. Let Λ be a (finite dimensional) central division algebra over K. So Λ represents a class [Λ] in B(K). The sequence
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تاریخ انتشار 2002