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In that case a quantitative measure of ramification is defined for Galois extensions, basically by asking how far the Galois group moves field elements with respect to the metric. A sequence of ramification groups is defined, reifying (amongst other things) wild (non-tame) ramification. This goes beyond the geometric analogue.
The tame ramification part ε is defined in terms of the reduction type: ε=0 for good reduction, ε=1 for multiplicative reduction and ε=2 for additive reduction. The wild ramification term δ is zero unless p divides 2 or 3, and in the latter cases it is defined in terms of the wild ramification of the extensions of K by the division points ...
In mathematics, the ramification theory of valuations studies the set of extensions of a valuation v of a field K to an extension L of K. It is a generalization of the ramification theory of Dedekind domains. [1] [2] The structure of the set of extensions is known better when L/K is Galois.
where is a measure of wild ramification. When F is a number field, the conductor ideal of A is given by = . Properties. A has good reduction at P if and only if = = ...
The multiplicity e j is called ramification index of P j over p. If it is bigger than 1 for some j, the field extension L/K is called ramified at p (or we say that p ramifies in L, or that it is ramified in L). Otherwise, L/K is called unramified at p. If this is the case then by the Chinese remainder theorem the quotient O L /pO L is a product ...
Researchers cited several studies to support the idea that people in affluent areas may view coyotes differently, including one from last year that used fieldwork in L.A. and conversations ...
Ramification (mathematics), a geometric term used for 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. Ramification (botany), the divergence of the stem and limbs of a plant into smaller ones; Ramification group, filtration of the Galois group of a local field ...
Scientists have recently discovered a new primate species in Myanmar’s central forest. However, the Popa langur, named after nearby Mount Popa, is tragically already on the verge of extinction.