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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Brian Conrad
Stanford University
MR ID: 637175
Reference #


Posted date
2017-01-09 06:19:54
Revised date
2020-03-06 20:00:26
Notes type
   Topics Course
      Algebraic Geometry
   Number Theory
      Algebraic Number Theory
   Representation Theory

Algebraic Groups I

This is a course on the general structure of linear algebraic groups over arbitrary fields, covering the standard material prior to the refined theory in the reductive case, using scheme-theoretic methods (flatness, infinitesimal criteria, etc.) at the level of a year-long course on schemes.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v3 PDF (1.1M) 03/09/20
Supplementary v3 PDF (280K) 03/06/20