In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing...
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Look up ramification in Wiktionary, the free dictionary. Ramification may refer to: Ramification (mathematics), a geometric term used for 'branching out'...
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from earlier resolutions of ramification as problematic for their own algorithms. Non-monotonic logic Ramification (mathematics) Nikos Papadakis "Actions...
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information on the ramification phenomena of the extension. In mathematics, the ramification theory of valuations studies the set of extensions of a valuation...
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In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and...
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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer...
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Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...
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List of algebraic number theory topics (category Mathematics-related lists)
Dirichlet's unit theorem Discriminant of an algebraic number field Ramification (mathematics) Root of unity Gaussian period Fermat's Last Theorem Class number...
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{\displaystyle \Omega _{X/Y}} is zero. Finite extensions of local fields Ramification (mathematics) Hartshorne 1977, Ch. IV, § 2. Grothendieck & Dieudonné 1967,...
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Branched covering (redirect from Ramification locus)
The set of exceptional points on W {\displaystyle W} is called the ramification locus (i.e. this is the complement of the largest possible open set W...
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Theory and Its Ramifications Journal of Logic and Analysis Journal of Mathematical Biology Journal of Mathematical Logic Journal of Mathematical Physics Journal...
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Torus (redirect from Torus (mathematics))
group is abelian). The 2-torus double-covers the 2-sphere, with four ramification points. Every conformal structure on the 2-torus can be represented as...
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f(z_{0})} is a positive integer called the ramification index of z 0 {\displaystyle z_{0}} . If the ramification index is greater than 1, then z 0 {\displaystyle...
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restriction of w to K is v. The set of all such extensions is studied in the ramification theory of valuations. Let L/K be a finite extension and let w be an extension...
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Galois module (redirect from Ramification of Galois representations)
by Emmy Noether (perhaps known earlier?). What matters here is tame ramification. In terms of the discriminant D of L, and taking still K = Q, no prime...
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when one is a ramified covering of the other. It therefore connects ramification with algebraic topology, in this case. It is a prototype result for many...
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Hasse–Arf theorem (redirect from Higher ramification groups)
proved by Cahit Arf. The theorem deals with the upper numbered higher ramification groups of a finite abelian extension L / K {\displaystyle L/K} . So assume...
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Prime number (redirect from Prime (mathematics))
ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in...
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Finite extensions of local fields (redirect from Ramification of local fields)
In algebraic number theory, through completion, the study of ramification of a prime ideal can often be reduced to the case of local fields where a more...
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In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field...
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Impredicativity (redirect from Predicative mathematics)
A prototypical example is intuitionistic type theory, which retains ramification (without the explicit levels) so as to discard impredicativity. The 'levels'...
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Glossary of number theory (category Glossaries of mathematics)
is three positive integers a, b, c such that a2 + b2 = c2. ramification The ramification theory. relatively prime See coprime. ring of integers The ring...
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Frank Calegari (category International Mathematical Olympiad participants)
ISSN 0020-9910. S2CID 8937648. Calegari, Frank; Emerton, Matthew (2005). "On the ramification of Hecke algebras at Eisenstein primes". Inventiones Mathematicae. 160...
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Superelliptic curve (section Ramification)
is the ramification index e ( P α , i ) {\displaystyle e(P_{\alpha ,i})} at each of the ( m , r α ) {\displaystyle (m,r_{\alpha })} ramification points...
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field theories and their main generalizations. In his study of infinite ramification theory, Fesenko introduced a torsion free hereditarily just infinite...
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Chemical & Earth Sciences Mathematical Reviews Zentralblatt MATH History of knot theory Journal of Knot Theory and Its Ramifications, SCImago, retrieved 2015-03-02...
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Artin–Schreier curve (section Ramification)
B} lies a single ramification point P α {\displaystyle P_{\alpha }} with corresponding different (not to confused with the ramification index) equal to...
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41403 Ogg, A. P. (1967), "Elliptic curves and wild ramification", American Journal of Mathematics, 89 (1): 1–21, doi:10.2307/2373092, ISSN 0002-9327,...
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algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field. Let K be a global field...
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Racks and quandles (redirect from Wrack (mathematics))
In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams...
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