# nLab standard conjectures

Standard conjectures on algebraic cycles consist of several conjectures brought up by Grothendieck on relation between algebraic cycles and Weil cohomology theories. They were also followed by “Beilinson’s dream” on motivic (c omplexes of) sheaves which comprise so called standard conjectures of Beilinson.

• A. Grothendieck, Standard Conjectures on Algebraic Cycles,, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford University Press, pp. 193–199, pdf
• Steven Kleiman, Algebraic cycles and the Weil conjectures, in: Dix exposés sur la cohomologie des schémas, North-Holland, pp. 359–386, 1968, MR0292838; The standard conjectures, Motives (Seattle, WA, 1991), Proc. of Symposia in Pure Math. 55, American Mathematical Society, pp. 3–20, 1994, MR1265519
• wikipedia standard conjectures on algebraic cycles