p-Adic Lie Groups

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The book delves into the geometric framework of manifolds over complete nonarchimedean fields, emphasizing tangent spaces and vector fields crucial for p-adic analysis. It provides a thorough introduction to locally analytic functions as topological vector spaces, essential for representation theory. The author establishes the analytic foundations for p-adic Lie groups and their Lie algebras. Notably, it presents Lazard's algebraic approach to compact p-adic Lie groups, introducing p-valuations and their implications for completed group rings, marking a significant contribution to the field.