This entry will be about the 1960 thesis of Pierre Gabriel, published in 1962 as
The article develops some of the central aspects of the theory of abelian categories canonized few years earlier by Grothendieck in Tohoku. Most important is an advanced theory of localization in the setting of abelian categories (extending ideas of Serre), and the applications to the study of rings and modules (where an alternative reconstructions via Gabriel filters is proposed), as well as of quasicoherent sheaves on schemes. It contains a remarkable reconstruction theorem: for any abelian category Gabriel introduces a spectrum whose points are indecomposable injectives. For a reasonable class of commutative schemes this gives a reconstruction of a scheme out of the abelian category of quasicoherent sheaves on the scheme (later extended to all schemes using different kind of spectra and in that generality known as the Gabriel-Rosenberg theorem). This article is one of the main precursors of a modern, categorically oriented, direction in noncommutative algebraic geometry.