2022.03.19 22:02

# [SNU Number Theory Seminar 2022.03.18] On p-rationality of $\mathbb{Q}(\zeta_{2l+1})^{+}$ for Sophie Germain primes $l$

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일정시작 2022-03-18 #FF5733
• Date :   3월 18일 (금) 4:00 PM

• Place :  27동 325호 (서울대학교)

• Speaker :  Donghyeok Lim (Ehwa Womans University)

• Title :  On p-rationality of $\mathbb{Q}(\zeta_{2l+1})^{+}$ for Sophie Germain primes $l$

• Abstract :  A number field F is called p-rational for an odd prime p, if the Galois group of the maximal pro-p extension of F that is unramified outside p is pro-p free. It was introduced by Abbas Movahhedi to find non-abelian number fields for which the Leopoldt conjecture at p is true. In this talk, we briefly explain the theory of p-rationality. We also show that if l is a Sophie Germain prime such that p is a primitive root modulo l, then Q(\zeta_{2l+1})^{+} is p-rational if p is less than 4l. We also give a heuristic evidence for the recent conjecture of Georges Gras that a number field is p-rational for all but finitely many primes p.

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