Manifolds over entire nonarchimedean fields including notions like tangent areas and vector fields shape a handy geometric language to precise the fundamental formalism of p-adic research. the quantity starts off with a self-contained and exact creation to this language. This comprises the dialogue of areas of in the community analytic features as topological vector areas, very important for purposes in illustration concept. the writer then units up the analytic foundations of the speculation of p-adic Lie teams and develops the relation among p-adic Lie teams and their Lie algebras. the second one a part of the booklet includes, for the 1st time in a textbook, an in depth exposition of Lazard's algebraic method of compact p-adic Lie teams, through his inspiration of a p-valuation, including its software to the constitution of accomplished team jewelry.
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