In this course we are going to follow closely SGA1 and SGA4 to develop an abstract framwork of fundamental groups and cohomology theory. To do this we first need a generalization of a topological space, and this would be the Grothendieck topology. The notion of sheaves on a topological space would be generalized to the notion of topos. The sheaf cohomology will be replaced by the derived category of a ringed topos. This general framwork serves like a machine: whenever one puts in a concrete Grothendieck topology one gets the corresponding cohomology theory out, and after some further work one may also get the corresponding fundamental group. In this course we are going to put in the étale topology in, and study the output, namely the étale cohomology and the étale fundamental group, which are also the most important output of this machine.
The prerequests for this course is a first course in algebraic geometry. A certain familiarity with the language of schemes and commutative algebra is prefered. But these will not be used to develop the general machine of cohomology theory and fundamental groups.
Every Tursday there will be a new exercise sheet. You can try to solve them, and if you have any questions please contact me at firstname.lastname@example.org.
Place (course): SR 130/A3 (Arnimallee 3)
Place (exercise): SR 130/A3 (Arnimallee 3)
Date: Wednesday 10:00-12:00 (course) and 14:00-16:00 (exercise)
First Appointment: 19.10.2016
Course Language: English