group scheme

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English

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Noun

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group scheme (plural group schemes)

  1. (category theory, scheme theory) A group object that is an object in a category of schemes; a scheme that has certain properties that generalise the concept of group.
    • 1973, Jean A. Dieudonné, Introduction to the Theory of Formal Groups, Marcel Dekker, page 6:
      It is instructive to give a few explicit examples of such[affine] group schemes:
    • 2013, Philippe Gille, Arturo Pianzola, Torsors, Reductive Group Schemes and Extended Affine Lie Algebras, American Mathematical Society, page 11:
      We will tend to use boldface characters, such as , for algebraic groups over , as also for group schemes over that are obtained from groups over . A quintessential example is . For arbitrary group schemes, or more generally group functors, over we shall tend to use german characters, such as .
    • 2014, J. S. Milne, “The Work of John Tate”, in Helge Holden, Ragni Piene, editors, The Abel Prize 2008-2012, Springer,, page 303:
      Every finite flat group scheme of order over is of the form for some triple , and is isomorphic to if and only if there exists an isomorphism from to carrying to and to .

Further reading

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