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Is it the letter dated in 27/08/1965 of Grothendieck where he presents to Serre the Standard conjectures on algebraic cycles?

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    $\begingroup$ A clue: p232 of books.google.co.uk/… $\endgroup$
    – user5117
    Commented Jul 24, 2014 at 15:18
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    $\begingroup$ I am not sure what you exactly ask. The standard conjectures of Grothendieck appear in the Proceedings of the 1968 Bombay Colloquium of Algebraic Geometry, see here. The letter you mention already discusses some of these conjectures or related questions, but go to the above mentioned paper for the full conjectures. $\endgroup$
    – abx
    Commented Jul 24, 2014 at 15:33

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The answer is yes. I just read the letter in the Grothendieck-Serre Correspondence volume, August 27, 1965, pages 232 to 235.

It is a very nice read, with quite a complete description of the full standard conjectures. Grothendieck goes on to formulate both the strong and weak Lefschetz standard conjecture, the Hodge standard conjecture, and also gives some details about their relation to the Weil conjecture, the Künneth formula for cycles, and the numerical equivalence conjecture.

This is not quite surprising, since his famous 1968 paper, in which he fully presents the conjectures, mentions:

"These [conjectures] are not really new, and they were worked out about three years ago independently by Bombieri and myself."

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