MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The tame quotient of the inertia group of $\mathbf Q_p$, say, is the profinite group generated by the Frobenius $\sigma$ and the monodromy $\tau$, subject to the relation $\tau^{p-1} [\tau, \sigma] = 1$.

Question: why is this second generator called a monodromy, or, more precisely what O.D.E. corresponds to this situation?

Related question: Katz, in "On the calculation of some differential Galois groups" suggests to think of the inertia group as being analogous to the Tannaka group of some category of certain $D$-modules. How does that idea relate to the above situation?

Thank you!

share|cite|improve this question
Dear Jakob -- In the analogous situation where the local field contains its residue field, such as $\mathbf{C}((t))$ or $\mathbf{F}_p((t))$, linear differential equations in the uniformizer are closely related to Galois theory, or at least the tame part. $\tau$ plays the role of a loop around a punctured disk. – JBorger Jun 15 '13 at 3:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.