Chathumini Kondasinghe, Temple University
This talk aims to explore how long exact sequences of group cohomology provide insights into field theory and elliptic curves. We begin with a proof of Hilbert's theorem 90, and then use the long exact sequence of Galois cohomology to establish Kummer theory for fields. In the second half, we will talk about the idea that goes into the proof of the weak Mordell-Weil theorem, a finiteness result for elliptic curves.