Motives

(Definition of Pierre Deligne)

Tuple of modules, rings, and comparison isomorphisms

(M_B, M_DR, M_A^f, M_cris,p, comp_DR,B, comp_A^f,B, comp_crip,p,DR, W, F_inf, F, \phi, \phi_p)

Where M_B, M_DR, M_A^f are modules with Betti cohomology, DeRham Cohomology, Crystalline Cohomology and Singular Cohomology

W, F are filtrations
Gal(Q',Q) action \phi on M_A^f and frobenius automorphism from \phi_p to M_cris,p