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

The answer is yes. I just read the letter in the GrothendieckSerre 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:


