### On reduction steps for Leopoldt's conjecture

Heilbronn Number Theory Seminar

26th October 2022, 4:00 pm – 5:00 pm

Fry Building, 2.04

Let p be a rational prime and let L/K be a Galois extension of number fields with Galois group G. Under some hypotheses, we show that Leopoldt's conjecture at p for certain proper intermediate fields of L/K implies Leopoldt's conjecture at p for L; a crucial tool will be the theory of norm relations in Q[G]. We also consider relations between the Leopoldt defects at p for intermediate extensions of L/K. We finally show that our results combined with some techniques introduced by Buchmann and Sands allow us to find infinite families of nonabelian totally real Galois extension of Q satisfying Leopoldt's conjecture for certain primes. This is joint work with Henri Johnston.

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