Eric Hsieh will give the talk on Monday, October 18 at 4:15 in Math 528. This lecture will be open to all.
Abstract: Let $X$ be a connected manifold, and $\tilde{X}$ be its universal covering, we know the deck transformation of $\tilde{X}$ over $X$ is isomorphic to $\pi_1(X)$. From this point of view, we can get the definition of the algebraic fundamental group for a connected scheme by introducing the notion of etale covering. The goal is to show that for a field $K$, $\pi_1(\Spec K)$ is the absolute Galois group of $K$ and we can see the relation between algebraic and topological fundamental groups from complex tori.
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