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Number Theory

Local algebraic theory

Lubin and Oort conjectures, automorphism group of a field of formal series, Nottingham group, ramification, non abelian class field theory.

Global algebraic theory and K-theory

Galois groups, Galois module structure, K-theory of rings of integers, genus formula for wild kernels, K-theory and Iwasawa theory.

Archimedean analytic theory

Asymptotic study of arithmetic functions, distribution of divisors, friable integers.

Ultrametric analytic theory

Frobenius structure of p-adic differential equations, multiplicative semi-normes, continuous endomorphisms of Hadamard algebras.