Mallory Dolorfino, University of Washington
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PDL C-401
Last week, we saw some strange and, from some points of view, undesirable qualities of the etale fundamental group. Namely, the etale fundamental group of a point is usually not trivial, and the etale fundamental group of SpecZ is 0. From a number theoretic perspective, these qualities of the etale fundamental group make it a great tool for studying the arithmetic properties of schemes. In this talk, we will elucidate this fact by computing the etale fundamental groups of certain fields, generalizing the fact about SpecZ to rings of integers in arbitrary number fields, and exploring the arithmetic implications of Grothendieck's section conjecture.
Zoom Link: https://washington.zoom.us/j/92849568892