Hasse arf theorem
Webof Helmut Hasse in 1937/38. Arf’s thesis [2] has become widely known, where he had obtained a generalization of a former theorem of Hasse about the ramification behavior of abelian number fields; today this is known as the “Hasse-Arf theorem”.2 His next paper, after his thesis, contains the “Arf invariant” which is our concern to-day. WebThe Hasse-Arf theorem states Theorem 1. With notations as above, assume moreover that G is an abelian p-group. Let s < t be two subsequent jumps of QjP; i.e., we have Gs % …
Hasse arf theorem
Did you know?
Webclassical Hasse- Arf theorem. Remark. One can define a naive Swan conductor [1, 6.7] as well. It also is an integer in the monogenic case but simply because it agrees with the … WebIn mathematics, specifically in local class field theory, the Hasse–Arf theorem is a result concerning jumps of the upper numbering filtration of the Galois group of a finite Galois …
WebDec 26, 1997 · In 1937 he went to the University of Göttingen to study for his doctorate under the supervision of Helmut Hasse. He completed his doctoral studies in 1938 … Webclassical Hasse-Arf theorem. Remark. One can define a naive Swan conductor [1, 6.7] as well. It also is an integer in the monogenic case but simply because it agrees with the …
WebNov 24, 2008 · We prove a Hasse-Arf theorem for the arithmetic ramification filtrations on G_K, except possibly in the absolutely unramified and non-logarithmic case, or p=2 and logarithmic case. As an application, we obtain a Hasse-Arf theorem for filtrations on finite flat group schemes over O_K. Submission history From: Liang Xiao [ view email ]
WebHasse–Arf theorem also holds in this context. Partial results in this direction were obtained by Spriano [5]. A proof of the Hasse-Arf theorem in equal characteristic that is strong enough to cover monogenic extensions was outlined at the 1999 Luminy conference on ramification theory. It was based on a technical analysis of a refinement [2,
WebMar 24, 2024 · A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the … botox injections portland oregonWebThe theorem of the title refers to the fact that the maximal abelian extension of a local field may be generated by roots of unity (for the unramified part) and roots of endomorphisms of a certain formal group… Expand View via Publisher Save to Library Create Alert Cite 14 Citations Citation Type More Filters hayes healy center notre dameWebHasse-Arf theorem if the Galois group G is an elementary-abelian group of expo-nent p, see Theorem 2 below. Our method also yields some weaker results in the case of arbitrary (abelian or non-abelian) p-groups G, see Theorem 3 below. Other basic ingredients in the proofs below are the transitivity of di erent exponents and Hilbert’s di erent ... hayes healy hallWebFeb 2, 2024 · The Hasse-Arf theorem [8, 1] says that if G= Gal(L/K) is abelian then every upper break of L/K is an integer. The Hasse-Arf theorem plays an important role in several areas of number theory. For instance, it is used in the construction of the Artin representation [2] and in Lubin’s proof of the local Kronecker-Weber theorem [10]. botox injections reno nvIn mathematics, specifically in local class field theory, the Hasse–Arf theorem is a result concerning jumps of the upper numbering filtration of the Galois group of a finite Galois extension. A special case of it when the residue fields are finite was originally proved by Helmut Hasse, and the general result was … See more Higher ramification groups The theorem deals with the upper numbered higher ramification groups of a finite abelian extension L/K. So assume L/K is a finite Galois extension, and that vK is a See more For non-abelian extensions the jumps in the upper filtration need not be at integers. Serre gave an example of a totally ramified extension with Galois group the quaternion group Q8 of order 8 with • G0 = Q8 • G1 = Q8 See more botox injections redlands caWebof Helmut Hasse in 1937/38. Arf’s thesis [2] has become widely known, where he had obtained a generalization of a former theorem of Hasse about the ramification behavior … botox injections prescott azWeb@article{Yoshida2008, abstract = {We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].}, affiliation = {Harvard University, Department of Mathematics, 1 Oxford Street, Cambridge, MA 02138, USA}, author = {Yoshida, Teruyoshi}, journal = {Annales de la … hayes healthcare llc