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Weber's class invariants revisited

Reinhard Schertz (2002)

Journal de théorie des nombres de Bordeaux

Let K be a quadratic imaginary number field of discriminant d . For t let 𝔒 t denote the order of conductor t in K and j ( 𝔒 t ) its modular invariant which is known to generate the ring class field modulo t over K . The coefficients of the minimal equation of j ( 𝔒 t ) being quite large Weber considered in [We] the functions f , f 1 , f 2 , γ 2 , γ 3 defined below and thereby obtained simpler generators of the ring class fields. Later on the singular values of these functions played a crucial role in Heegner’s solution [He] of the class...

Which weakly ramified group actions admit a universal formal deformation?

Jakub Byszewski, Gunther Cornelissen (2009)

Annales de l’institut Fourier

Consider a representation of a finite group G as automorphisms of a power series ring k [ [ t ] ] over a perfect field k of positive characteristic. Let D be the associated formal mixed-characteristic deformation functor. Assume that the action of G is weakly ramified, i.e., the second ramification group is trivial. Example: for a group action on an ordinary curve, the action of a ramification group on the completed local ring of any point is weakly ramified.We prove that the only such D that are not pro-representable...

Why is the class number of ( 11 3 ) even?

F. Lemmermeyer (2013)

Mathematica Bohemica

In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.

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