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- what does it mean for a prime at infinity to ramify?
The above definition of ramification for real places is the usual one, justified e g by the ramification index 2 which appears in a complex valuation over a real one (see Joequinn's answer) However the same phenomenon could also be interpreted as the splitting of the real place under the complex one
- algebraic number theory - Decomposition group and inertia group . . .
Explore related questions algebraic-number-theory ramification See similar questions with these tags
- Standard Definition of Ramified (or Branched) Cover of Topological 3 . . .
The definition should allow for ramification along an embedded graph, not just a disjoint union of circles, and outside of the ramification locus the map should of course just be a topological covering map (probably of finite degree) EDIT – It seems I was not clear enough originally
- Vague definitions of ramified, split and inert in a quadratic field
Yes, these are very important definitions in algebraic number theory What is vague about them?
- Definition of Galois representation unramified at a prime.
In J Weinstein's note: Reciprocity laws and Galois representations: recent breakthroughs, section 3 3, a Galois representation that is unramified at a prime $\\mathfrak{p}$ is defined in a differen
- algebraic geometry - Galois extension and morphism of curves . . .
By the Riemann-Hurwitz formula the degree of the ramification divisor is 4, hence $\phi$ can ramify in three possible ways: (a) two points of ramification index 3; (b) one point of ramification index 3 and two point of ramification index 2; (c) four points of ramification index 2
- Understanding the Inertia Group in Ramification Theory
23 I am a beginner student of Algebraic Number Theory and I am starting to learn ramification theory (of global fields) My question asks for motivation for a definition I was given Let K K be an algebraic number field, OK O K its ring of integers, L K L K a Galois extension and OL O L the integral closure of OK O K in L L
- Degree of an holomorphic map and ramification points
Suppose, for instance, that you calculated the degree of $f$ as $3$ and found all three ramification points The multiplicity of $f$ at $0$ is just the order of the zero, namely $3$
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