In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation...
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geometry (Hasse principle), and to local zeta functions. Hasse was born in Kassel, Province of Hesse-Nassau, the son of Judge Paul Reinhard Hasse, also written...
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Algebraic number field (section Hasse principle)
solution is also a solution in all completions. The local-global principle or Hasse principle asserts that for quadratic equations, the converse holds, as...
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Martin Kneser, Günter Harder and Vladimir Chernousov (1989) proved the Hasse principle: for a simply connected semisimple group G over k, the map H 1 ( k...
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Hardy–Littlewood circle method. For example, the Hasse–Minkowski theorem says that the Hasse principle holds for quadric hypersurfaces over a number field...
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theorems of Helmut Hasse that are sometimes called Hasse's theorem: Hasse norm theorem Hasse's theorem on elliptic curves Hasse–Arf theorem Hasse–Minkowski theorem...
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Adele ring (section Hasse principle)
the Hasse principle for quadratic forms. For polynomials of degree larger than 2 the Hasse principle isn't valid in general. The idea of the Hasse principle...
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P-adic analysis (section Local–global principle)
this is both needed and worthwhile." Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer...
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The initial result of this type was Eisenstein's theorem. Hasse principle The Hasse principle states that solubility for a global field is the same as...
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reductive groups. Kottwitz (1988) proved it for all groups satisfying the Hasse principle, which at the time was known for all groups without E8 factors. V....
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{\displaystyle {\sqrt {3}},} centered at the origin. More generally, the Hasse principle allows deciding whether a homogeneous Diophantine equation of degree...
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the Hasse principle, capable of yielding quantitative information. If d is fixed and k is small, other methods are required, and indeed the Hasse principle...
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solutions) provides also sufficient conditions, one says that the Hasse principle holds: this is the best possible situation. It does for quadratic forms...
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published his work in 1923 and 1924. See Hasse principle, Hasse–Minkowski theorem. The local-global principle says that a general result about a rational...
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D., but joint work with Cassels produced numerical examples on the Hasse principle for cubic surfaces. He subsequently went into computer science. He...
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The Hasse principle would predict that if X has a rational point over all completions Kv of K, then X has a K-rational point. The Hasse principle holds...
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a variety X over a global field, which measures the failure of the Hasse principle for X. If the value of the obstruction is non-trivial, then X may have...
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Idele group Idele class group Adelic algebraic group Global field Hasse principle Hasse–Minkowski theorem Galois module Galois cohomology Brauer group Class...
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conjecture abc Conjecture Catalan's conjecture Pillai's conjecture Hasse principle Diophantine set Matiyasevich's theorem Hundred Fowls Problem 1729 Davenport–Schmidt...
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_{i\in I}k.} Consequently, (αi)i∈I = (0)i∈I. QED. Covering system Hasse principle Residue number system Katz 1998, p. 197 Dence & Dence 1999, p. 156...
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their reductions modulo some or all prime numbers. See, for example, Hasse principle. Many recent developments of algebraic geometry were motivated by the...
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In order theory, a Hasse diagram (/ˈhæsə/; German: [ˈhasə]) is a type of mathematical diagram used to represent a finite partially ordered set, in the...
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In mathematics, the Hasse–Witt matrix H of a non-singular algebraic curve C over a finite field F is the matrix of the Frobenius mapping (p-th power mapping...
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in algebraic geometry. His work has focused on rational points, the Hasse principle, the Manin obstruction, exponential sums, and error-correcting codes...
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mathematics professor". The Daily Illini. Retrieved 8 December 2021. "Hasse Principle – Numberphile". YouTube. 1 June 2016. Haran, Brady. "Tom Crawford on...
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Venkatesh, jointly with Jordan Ellenberg, made significant progress on the Hasse principle for integral representations of quadratic forms by quadratic forms...
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the role of the Brauer group in accounting for obstructions to the Hasse principle via Grothendieck's theory of global Azumaya algebras, setting off a...
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analog communications channel. Named for Ralph Hartley (1888–1970). Hasse principle is the idea that one can find an integer solution to an equation by...
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K-rational point. Thus, the group measures the extent to which the Hasse principle fails to hold for rational equations with coefficients in the field...
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In number theory, the Hasse norm theorem states that if L/K is a cyclic extension of number fields, then if a nonzero element of K is a local norm everywhere...
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