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16 votes

Are there "motivic" proofs of Weil conjectures in special cases?

The paper by Manin is MR0258836 Manin, Ju. I. Correspondences, motifs and monoidal transformations. Mat. Sb. (N.S.) 77 (119) 1968 475--507 where he uses motives to prove the Weil conjectures for un …
Richard Borcherds's user avatar
19 votes

Weil conjecture for algebraic surfaces

Deligne (La conjecture de Weil pour les surfaces $K3$. (French) Invent. Math. 15 (1972), 206--226 MR0296076 ) gave a proof for K3 surfaces shortly before his proof of the general case, but it is not e …
Richard Borcherds's user avatar