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Abelian group Abelian variety affine algebraic group algebraic number algebraic number field algebraic variety Amer analytic set automorphism axiom Banach space boundary called canonical closed coefficients cohomology compact computation condition connected continuous convergence convex coordinate corresponding curve defined denote differential equations dimension dimensional divisor domain element elliptic equivalent ergodic Euclidean exists fiber fiber bundle finite number formula func function geometry given group G Hilbert holomorphic homeomorphic ideal integral invariant irreducible isomorphic Lie group linear space manifold mapping Math mathematics matrix measure method metric morphism n-dimensional neighborhood nonsingular number field obtained open set ordinal number phism plane polynomial prime problem properties quotient real numbers representation resp respect Riemann ring satisfies sequence sheaf singular solution Springer structure subgroup subset subspace surface tangent theorem theory tion tive topological space transformation unique Univ variables vector bundle vector field zero