
Date : 3월 18일 (금) 4:00 PM

Place : 27동 325호 (서울대학교)

Speaker : Donghyeok Lim (Ehwa Womans University)

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

Abstract : A number field F is called prational for an odd prime p, if the Galois group of the maximal prop extension of F that is unramified outside p is prop free. It was introduced by Abbas Movahhedi to find nonabelian number fields for which the Leopoldt conjecture at p is true. In this talk, we briefly explain the theory of prationality. 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 prational if p is less than 4l. We also give a heuristic evidence for the recent conjecture of Georges Gras that a number field is prational for all but finitely many primes p.