mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes...
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mathematics, Hasse invariant may refer to: Hasse invariant of an algebra Hasse invariant of an elliptic curve Hasse invariant of a quadratic form This disambiguation...
183 bytes (56 words) - 17:39, 28 December 2019
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x...
33 KB (4,554 words) - 17:42, 31 May 2024
The Hasse–Minkowski theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only...
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1923 Hasse diagram Hasse invariant of an algebra Hasse invariant of an elliptic curve Hasse invariant of a quadratic form Artin–Hasse exponential Hasse–Weil...
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Cahit Arf (category Academic staff of Istanbul University)
October 1910 – 26 December 1997) was a Turkish mathematician. He is known for the Arf invariant of a quadratic form in characteristic 2 (applied in knot...
10 KB (991 words) - 03:55, 21 August 2024
Witt group (redirect from Height of a field)
well-defined. The Hasse invariant of a quadratic form is again a well-defined function on Witt classes with values in the Brauer group of the field of definition...
21 KB (3,169 words) - 09:30, 25 April 2024
Emmy Noether (category Academic staff of the University of Göttingen)
a finite basis (with one element) for the invariants of binary quadratic forms. Noether's advisor, Paul Gordan, was known as the "king of invariant theory"...
127 KB (14,690 words) - 09:15, 23 August 2024
Multiplicative order Discrete logarithm Quadratic residue Euler's criterion Legendre symbol Gauss's lemma (number theory) Congruence of squares Luhn formula Mod n...
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Adelic algebraic group (redirect from Group of ideles)
theory, particularly for the theory of automorphic representations, and the arithmetic of quadratic forms. In case G is a linear algebraic group, it is an...
7 KB (935 words) - 20:05, 12 January 2024
Stiefel–Whitney class (section Related invariants)
Stiefel–Whitney classes for quadratic forms over fields, the first two cases being the discriminant and the Hasse–Witt invariant (Milnor 1970). For a real vector bundle...
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group then the corresponding invariant is essentially the Hasse−Witt invariant. If G is the orthogonal group of a quadratic form in characteristic not 2,...
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defined for a binary quadratic form. It is a special case of a Hasse–Weil L-function. The natural definition of L(E, s) only converges for values of s in the...
24 KB (2,946 words) - 11:02, 31 May 2024
Brauer group (category Topological methods of algebraic geometry)
injectivity of the left arrow is the content of the Albert–Brauer–Hasse–Noether theorem. The fact that the sum of all local invariants of a central simple...
22 KB (2,941 words) - 20:50, 16 July 2024
Albert–Brauer–Hasse–Noether theorem, saying that a central simple algebra over a number field is determined by its local invariants. Building on the Hasse principle...
55 KB (7,845 words) - 18:28, 24 April 2024
the j-invariant of the curve lies in a quadratic extension of the prime field of K, a finite field of order p2. Suppose E is in Legendre form, defined...
13 KB (2,235 words) - 09:19, 3 July 2024
The canonical height on an abelian variety is a height function that is a distinguished quadratic form. See Néron–Tate height. Chabauty's method Chabauty's...
37 KB (4,753 words) - 14:39, 23 July 2024
(number theory) Sylvester pentahedral theorem (invariant theory) Sylvester's law of inertia (quadratic forms) Sylvester–Gallai theorem (plane geometry) Symmetric...
73 KB (6,015 words) - 12:17, 2 August 2024
F4 (mathematics) (section F4 polynomial invariant)
{1}{2}}\\\end{bmatrix}}} The Hasse diagram for the F4 root poset is shown below right. Just as O(n) is the group of automorphisms which keep the quadratic polynomials...
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Elliptic curve (redirect from Weierstrass form)
important ingredient is a function of a complex variable, L, the Hasse–Weil zeta function of E over Q. This function is a variant of the Riemann zeta function...
54 KB (8,301 words) - 16:50, 17 August 2024
value of the Arf invariant of a certain quadratic form Q with values mod 2. Thus in case of g = 3 and a plane quartic curve, there were 28 of one type...
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Manjul Bhargava (category Members of the United States National Academy of Sciences)
classical law for composition of binary quadratic forms to many other situations. One major use of his results is the parametrization of quartic and quintic orders...
24 KB (2,103 words) - 14:34, 21 August 2024
Hermann Minkowski (category Academic staff of the University of Königsberg)
arithmetic of quadratic forms, especially concerning n variables, and his research into that topic led him to consider certain geometric properties in a space...
21 KB (1,924 words) - 23:34, 24 August 2024
original quadratic reciprocity law can be hard to see. The class number formula relates many important invariants of a number field to a special value of its...
40 KB (5,798 words) - 13:01, 5 July 2024
Field (mathematics) (redirect from Additive group of a field)
local–global principle. For example, the Hasse–Minkowski theorem reduces the problem of finding rational solutions of quadratic equations to solving these equations...
87 KB (10,299 words) - 08:01, 21 August 2024
a group and showing its size is such that p {\displaystyle p} is prime. For ECPP the group is an elliptic curve over a finite set of quadratic forms such...
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Formal group law (redirect from Height of a formal group law)
n-dimensional Lie algebra over the ring R, defined in terms of the quadratic part F2 of the formal group law. [x,y] = F2(x,y) − F2(y,x) The natural functor...
25 KB (3,592 words) - 07:40, 16 August 2024
Counting points on elliptic curves (redirect from Point counting of elliptic curves)
make use of the fact that groups of the form E ( F q ) {\displaystyle E(\mathbb {F} _{q})} are subject to an important theorem due to Hasse, that bounds...
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Algebraic number field (redirect from Degree of a number field)
{\displaystyle d} , the quadratic field Q ( d ) {\displaystyle \mathbb {Q} ({\sqrt {d}})} is a number field obtained by adjoining the square root of d {\displaystyle...
52 KB (8,407 words) - 17:41, 28 August 2024
David Hilbert (category Foreign associates of the National Academy of Sciences)
range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry...
58 KB (6,933 words) - 06:56, 20 August 2024