Title: What is the etale fundamental group?
Speaker: Marc Hoyois
Speaker Info: 3rd Year Graduate Student
This will be an elementary expository talk on the etale fundamental group. The etale fundamental group is a schematic invariant which plays a similar role as the fundamental group in topology. It agrees with the latter for varieties over the complex numbers, but over non-algebraically closed fields (like number fields) it also contains a lot of interesting arithmetic information. I will start by defining and illustrating the notion of etale morphism. I will briefly recap the theory of covering spaces in topology to motivate the definition of the etale fundamental group, and I will give several examples.Date: Tuesday, February 14, 2012