STNB2023(36a edició)
On reduction steps for Leopoldt's conjecture
Ponents
Fabio Ferri
Resum
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 idempotent 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.
Fitxers
No hi ha fitxers per descarregar
Compte
Llengües: