Spring 2012 MATH 274 001 LEC

Topics in Algebra
001 LECMWF 11-12P 31 EVANSBAKER, M54551
Units/CreditFinal Exam GroupEnrollment
4NONELimit:24 Enrolled:11 Waitlist:0 Avail Seats:13 [on 05/03/12]
Additional Information: 

Office: 999 Evans
Office Hours: TBA
Prerequisites: Math 256
Required Text: none
Recommended Reading: Vladimir Berkovich, Spectral Theory and Analytic Geometry over Non-Archimedean Fields
Syllabus: Non-Archimedean geometry is motivated by the desire to develop a theory of analytic spaces over non-Archimedean (for example p-adic) fields analogous to the classical theory of complex manifolds (or, more generally, complex analytic spaces). There are several different approaches to the subject, including Tate's theory of rigid analytic spaces, Raynaud's theory of admissible formal schemes, Berkovich's theory of non-Archimedean analytic spaces, and Huber's theory of adic spaces. We will touch on all of these, focusing mainly on Berkovich's theory. We will also discuss (in varying levels of detail) applications of non-Archimedean geometry to areas such as Galois representations, tropical geometry, and dynamical systems. Students will be expected to be familiar with the basics of scheme theory (as covered in Chapter II of Hartshorne) and we will present many of the foundational results concerning affinoid algebras without proof, but otherwise we will try to keep the material relatively self-contained.
Grading: Students will be expected to help write lecture notes which will be made available to the public at the end of the course. Grades will be based on class participation, assistance in writing up notes based on the lectures, and suggested improvements to the lecture notes.
Homework: see above