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1
The Theory of Algebraic Number Fields
It is now easy to recognise the characteristic property of the ramification group: it
is the following. Theorem 73. The ramification group consists precisely of the
automorphisms s such that sQ = Q (mod ^32) for all integers Q of K Proof. Let Q
be ...
2
Ramification Theoretic Methods in Algebraic Geometry
CHAPTER I: GENERAL RAMIFICATION THEORY Summary . Let A be a domain
integrally closed in its quotient field K, let K* be a finite separable algebraic
extension of K and let A* be the integral closure of A in K*. Let [K* : K] = n. Let W
and ...
Shreeram Shankar Abhyankar, 1959
3
Ramification of Primes in Fields of Moduli of Three-Point Covers
We examine in detail the stable reduction of three-point G-Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup.
4
Nevanlinna’s Theory of Value Distribution: The Second Main ...
then the integer (p — 1) is called the ramification index of / at CQ- Note that if / is
analytic, then / ramifies precisely at the zeros of /', and if ZQ is a ramification point
then its ramification index is given by ord1n/'. If /(CD) = oc. then one must look at ...
William Cherry, Zhuan Ye, 2001
5
Algebraic Number Theory
Let R and S be as above and let fy be a prime ideal of S. 1) The prime divisors of
p := tynR in S are the prime ideals gty for g e G. These prime ideals have
common ramification index e and inertia degree f. 2) The decomposition group
Gv has ...
6
Canadian Journal of Mathematics
RAMIFICATION. THEORY. FOR. VALUATIONS. OF. ARBITRARY. RANK.
MURRAY A. MARSHALL Throughout, we consider a finite Galois extension L\K
of non-archimedian valued fields which are maximally complete [2, Chapter 2].
7
Arithmetic Fundamental Groups and Noncommutative Algebra: ...
going to the Galois closure. (The distinction between absolute and inner Hurwitz
spaces: [BF, §3.5] captures this.) We define an explicit open subset P(TV) of
affine space parametrizing local field extensions with ramification data R (§2. §3).
Michael D. Fried, Yasutaka Ihara
8
Arithmetic, Geometry, Cryptography and Coding Theory
Let A„ = PTM+ P2TM denote the discriminant divisor (branch locus) of fn and let
Diff(/„) = Q1+Q2 its different divisor (ramification locus). Then by Proposition 6.7
we know that either Pf ^ P2TM or that Pf = P2TM = 0E and Q? ^ Q% (Case (3)).
Ramification Problem Minsky (1961) noted something similar to the frame and
ramification problems: One problem that has been a great nuisance to us arises
in connection with nonmathematical problems in which actions affect the state of
...
10
Relations Related to Betweenness: Their Structure and ...
37), we shall call its equivalence classes the cones below E. (Note, however, that
Droste uses this terminology only in case E is a ramification point as defined
below.) Cones in an upper semilinearly ordered set A can be characterised as ...
Samson Adepoju Adeleke, P. M. Neumann, 1998
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Decline of the West: Seven strategic ramifications of Crimea's return …
Crimea's March 16, 2014, referendum to join Russia — there were only two options: join now, or join later — marked a significant watershed in the ... «World Tribune, 3월 14»
