MOTIVE

Motive

In algebraic geometry, a motive denotes 'some essential part of an algebraic variety'. To date, pure motives have been defined, while conjectural mixed motives have not. Pure motives are triples , where X is a smooth projective variety, p : X ⊢ X is an idempotent correspondence, and m an integer. A morphism from to is given by a correspondence of degree n – m.

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motive

Noun

  1. An idea or communication that makes one want to act, especially from spiritual sources; a divine prompting.
  2. An incentive to act in a particular way; a reason or emotion that makes one want to do something; anything that prompts a choice of action.
  3. A limb or other bodily organ that can move.
  4. Something which causes someone to want to commit a crime; a reason for criminal behaviour.
    What would his motive be for burning down the cottage?
    No-one could understand why she had hidden the shovel; her motives were obscure at best.
  5. A motif.
  6. A motif; a theme or subject, especially one that is central to the work or often repeated.
    If you listen carefully, you can hear the flutes mimicking the cello motive.

Verb

  1. To prompt or incite by a motive or motives; to move.

Adjective

  1. Causing motion; having power to move, or tending to move; as, a motive argument; motive power.
  2. Relating to motion and/or to its cause


The above text is a snippet from Wiktionary: motive
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