## Annals of Mathematics |

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abelian algebra arbitrary assume belongs boundary bounded coefficients cohomology commutative compact space complex condition congruence relation consider constant continuous convergence convex subgroup COROLLARY corresponding curve cyclic defined definition denote differential dimension dimensional domain equation equivalent exists finite number follows fonctionnelles function g-simplex Galois group given Hence hermitian Hilbert space holds homology homomorphism homotopy groups Hopf invariant implies infinite integral invariant isomorphic kernel lattice Lemma Let G Lie group linear linear subspaces LP(E Math matrix maximal minimal elements mod q multiplication norm obtain open set operators polynomials positive numbers prime proof of Theorem properties prove real numbers relation relational algebra relatively complemented relatively complemented lattice represents satisfying semi-simple sequence simple simplex simplicial map singular subgroup of G subset subspaces Suppose Theorem theory tion topologie ultra-forte unique values vector space vertex zero