The Abelian Varieties from the Algebraic Viewpoint; and Related Questions

Abstract

The theory of the Abelian varieties from the transcendental standpoint is classical this field has been recently reviewed by Igusa [3], A. Weil [4], Chow [6] : see (XI, 2) ; the outstanding classical contributions are due to Picard, Poincaré;, Enriques, Castelnuovo, Severi and Lefschetz: see e. g. the report [b] of Lefschetz}: the Abelian varieties considered in an abstract, purely algebraic manner, have been investigated only recently, giving rise to a beautiful chapter in algebraic geometry, whose fundamental ideas and general methods are chiefly due to A. Weil {see the treatises [b, c] of A. Weil} and whose applications are chiefly linked with the names of Chow {see Chow [6, 7, 8, 9]}, Matsusaka {see Matsusaka [3, 4, 5, 6, 7, 8]}, Néron {see Néron [1, 2]} and Samuel {see Néron and Samuel [1]}.