Grothendieck’s Mysterious Functor.
For an abelian variety X with good reduction over a p-adic field K, Alexander Grothendieck reformulated a theorem of Tate’s to say that the crystalline cohomology H1(X/W(k)) ⊗ Qp of the special fiber (with the Frobenius endomorphism on this group and the Hodge filtration on this group tensored with K) and the p-adic étale cohomology H1(X,Qp) (with the action of the Galois group of K) contained the same information. Both are equivalent to the p-divisible group associated to X, up to isogeny. Grothendieck conjectured that there should be a way to go directly from p-adic étale cohomology to crystalline cohomology (and back), for all varieties with good reduction over p-adic fields.[7] This suggested relation became known as the mysterious functor.
—from Wikipedia.
The Burmese Ferret-Badger, of Burma 
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