Ramification of Quaternion Algebras over Stable Elliptic SurfacesReport as inadecuate




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* Corresponding author 1 Géométrie IECL - Institut Élie Cartan de Lorraine

Abstract : The aim of this work is to study the ramification of quaternion algebras over the function field of a stable elliptic surface, in particular over the field of complex numbers. Over number fields there are criteria for the ramification of quaternion algebras such as the tame symbol formula. We study how this formula can be interpreted in a geometrical way, and how the ramification relates to the geometry of the surface. In particular, we consider stable complex elliptic surfaces that have four 2−torsion sections.

Keywords : Elliptic surfaces Brauer group Quaternion algebras





Author: Arvid Perego -

Source: https://hal.archives-ouvertes.fr/



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