Understanding Ramification Points - Mathematics Stack Exchange I really don't understand how to calculate ramification points for a general map between Riemann Surfaces If anyone has a good explanation of this, would they be prepared to share it? Disclaimer:
Understanding the Inertia Group in Ramification Theory Yes And i know about the fundamental identity But I don't know exactly how is the inertial degree related to the inertia group, even though I can imagine it being the galois group of the extension of residue fields or something like this
How we can know the ramification ideals geometrically? How to actually compute the ramification index and inertia degree in practice is a whole other matter—my answer is just meant to give the abstract connection to geometry and some intuition about how it relates to the classical notion of ramification
Motivation for considering the upper numbering of ramification groups This definition makes sense by Herbrand's theorem, which tells us that we get a projective system to take the limit of In this way, the upper ramification groups are far more natural than the lower ramification groups The lower ramification groups have the advantage that they are easier to define and are sufficient for finite extensions
Branched cover in algebraic geometry - Mathematics Stack Exchange Many of these references eventually mention "branch" or "ramification" in passing or loosely, as if assuming the reader knows about it So my questions are: What are the definitions of "branched covering" and "ramification"? What is the map $\pi$ explicitly? Is there a code of ethics among algebraic geometers to make simple things harder for