Introduction to p-adic Hodge Theory
| Math 162b | |
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Topics in Number Theory Introduction to p-adic Hodge Theory |
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| Winter 2011-12 | |
Instructor: Andrei Jorza, 280 Sloan,
626-395-4369, ajorza@caltech.edu |
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This course
is intended as an introduction to the study of continuous Galois
representations of the absolute Galois group of Q_p acting on finite
dimensional Q_p vector spaces via p-adic Hodge theory.
We will study the big rings of Fontaine: B_HT, B_dR, B_cris, B_st and linear algebra data associated to p-adic Galois representations using them; we will also study general Galois representations using the theory of (phi, Gamma)-modules and fields of norms. Time permitting we will also look at some recent results on congruences between Galois representations, using integral p-adic Hodge theory. Although the p-adic Hodge theory of Galois representations was inspired by that of algebraic varieties over Q_p, this course will not require knowledge of advanced algebraic geometry. Knowledge of local class field theory (math 160b, which can be taken concomitantly) will be assumed. |
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A tentative syllabus.
A road map for p-adic Hodge theory, a subset of which we will loosely follow. The first lecture, which was an a motivating overview of p-adic Hodge theory. Lecture notes |
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Grade:
For students requiring a grade there will be biweekly homework. The final grade will be based on the homeworks. |
The most useful reference for the course is:
Other useful references:
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