Algebraic Groups - James Milne

Algebraic GroupsThe theory of group schemes offinite type over a MilneVersion 20, 2015An Algebraic group is a matrix group defined by polynomial conditions. More abstractly,it is a group scheme of finite type over a field. These notes are a comprehensive modernintroduction to the theory of Algebraic Groups assuming only the knowledge of algebraicgeometry usually acquired in a first is still only a preliminary version, but is the last before the final version. It will berevised again before publication. In particular, repetitions, references to my website, andnotational inconsistencies will be removed; exercises and examples will be added; errorswill be corrected. The final version will be more tightly written, and will include 500 pages+ front matter.

algebraic geometry, but with minimal prerequisites. It has been clear for fifty years that such a work has been needed. 1. When Borel, Chevalley, and others introduced algebraic geometry into the theory of algebraic groups, the foundations they used were those of the period (e.g.,Weil1946), and most subsequent

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  Group, Geometry, Algebraic geometry, Algebraic, Algebraic groups

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