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Motives — Grothendieck's Dream
www.jmilne.orgMotives — Grothendieck’s Dream James S. Milne April 24, 2012; v2.04 Abstract Grothendieck introduced the notion of a “motif” in a letter to Serre in 1964.
Alexandre Grothendieck’s EGA V - James Milne
www.jmilne.orgwhere S0 = Pv and ˘is the diagonal section so that H˘ = H, in this case one observes (up to better notations to be suggested by Dieudonn e) that Y = Y˘.In the general case of a ˘:S 0!Pv, one has therefore also Y˘ = Yxv P S. Finally if F is a sheaf of modules4 over Xwe denote by G˘ its inverse image over Y˘ by Gits inverse image over Hso that one also has G˘ = G