Weak approximation and non-abellian fundamental groups
Weak Néron models for cubic polynomial maps over a non-Archimedean field
Weber's class invariants revisited
Let be a quadratic imaginary number field of discriminant . For let denote the order of conductor in and its modular invariant which is known to generate the ring class field modulo over . The coefficients of the minimal equation of being quite large Weber considered in [We] the functions 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...
Weil-numbers and CM-fields (I).
Which weakly ramified group actions admit a universal formal deformation?
Consider a representation of a finite group as automorphisms of a power series ring over a perfect field of positive characteristic. Let be the associated formal mixed-characteristic deformation functor. Assume that the action of 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 that are not pro-representable...
Why is the class number of even?
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.
Wiles dokázal Taniyamovu hypotézu; důsledkem je Fermatova věta
Winding quotients and some variants of Fermat's Last Theorem.