On Vandiver's conjecture and Zp-extensions of Q(ζpn)

✍ Scribed by Ina Kersten; Johannes Michaliček

Publisher: Elsevier Science
Year: 1989
Tongue: English
Weight: 747 KB
Volume: 32
Category: Article
ISSN: 0022-314X
DOI: 10.1016/0022-314x(89)90091-7

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For each prime p in a certain family of odd primes, we construct an S 4 extension of Q unramified outside p. We show that for all p#3 (mod 8) in our family, this S 4 extension embeds in an S 4 extension, which is also unramified outside p. Invoking Serre's conjecture (in a proven case) allows us to