Fall 2017: Rational Points on Varieties


Organizers
Jen BergAnastassia Etropolski
Time
Tuesday, 10:30 - 11:30am
Room
HBH 22
Text
Rational points on varieties, by Bjorn Poonen

Calendar

Week Date Topic and Exercises
Week 1 9/5 Organizational Meeting
Week 2 9/12 Read Sections 1.3 and 1.5 and do exercises 1.9 - 1.11 as well as 1.20, 1.23, 1.25, and 1.28a. (Note: Exercises 1.14 - 1.29 are all for Section 1.5, and you can do others if you feel inspired. For example, 1.14, 1.15, and 1.21.)
Week 3 9/19 We will go over the problems from Section 1.5 in detail and finish going through the ideas in that section. You should also start reading Chapter 4 to familiarize yourself with the definitions and theorems. We will discuss its content the following week. If you have time, you should also take a look at these exercises.
Week 4 9/26 This week we'll go over twists and descent and work through exercise 4.3 as motivation for the Sections 4.1 - 4.4.
Week 5 10/3 Read Sections 4.5 - 4.6 and do exercises 4.2, 4.5, 4.6, and 4.7.
No meeting 10/10 Midterm Recess
Week 6 10/17 Skim chapters 5 and 6 to familiarize yourself with the objects. Pay special attention to: Group Schemes/Varieties, the Functor of Points, Frobenius, Smoothness (also go back to 3.5 for this), Torsors, Grothendieck Topologies, and the Brauer Group. We'll revisit these topics in more detail later!
Week 7 10/24 Read Chapter 6 up to Section 6.4.3.
Week 8 10/31 Read Sections 5.1 and 5.2 and do exercises 5.3, 5.4.
Week 9 11/7 Seminar Canceled
Week 10 11/14 Continue going through 5.1 and 5.2
Week 11 11/21 This week we'll go over exercises 5.3, 5.4, and maybe 5.11.
Week 12 11/28