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Pré-Publication, Document De Travail Année : 2021

ON THE p-CLASS GROUP STABILITY ALONG CYCLIC p-TOWERS OF A NUMBER FIELD

Résumé

Let k be a number field and let p ≥ 2 be a prime number. We call K/k a (pro)-cyclic p-tower if Gal(K/k)~ Z/p^N Z or Z_p. We give an elementary proof of a stability theorem about generalized p-class groups in the tower (Main Theorem 3.1). This result, using generalizations of Chevalley's formula (Gras, J. Math. Soc. Japan 46(3) (1994), Proc. Math. Sci. 127(1) (2017)), finds again or generalizes results by Fukuda (1994), Li--Ouyang--Xu--Zhang (2020), Mizusawa--Yamamoto (2020) and many others proving particular cases from Iwasawa's theory, pro-p-group theory or specific methods.
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Dates et versions

hal-03155190 , version 1 (01-03-2021)
hal-03155190 , version 2 (21-03-2021)
hal-03155190 , version 3 (31-03-2021)
hal-03155190 , version 4 (19-05-2021)
hal-03155190 , version 5 (12-08-2021)

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Georges Gras. ON THE p-CLASS GROUP STABILITY ALONG CYCLIC p-TOWERS OF A NUMBER FIELD. 2021. ⟨hal-03155190v1⟩
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