Olivetti Club

Nicole JohnsonCornell University
Field extensions, when we can get them, and what they look like

Tuesday, October 31, 2023 - 4:35pm
Malott 406

In this talk I will present a theorem of Gras and Munnier that tells us when we can get a $\mathbb{Z}/p\mathbb{Z}$- extension of a number field ramified exactly as a set $S$ of primes (or, more vaguely, when we can find field extensions of a certain size with certain properties). We will discover the theory in the context of quadratic extensions of $\mathbb{Q}$ and show how this aligns with the more general case.