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Results tagged with quadratic-forms
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user 51251
Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
2
votes
1
answer
200
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u-Invariants of p-adic function fields
In his Paper "Fields of u-invariant 9" Oleg Izhboldin points out that for a algebraic closed, finitely generated field $k$ we have $u(k)= 2^{cd(k)}$. In particular we have
$u(\mathbb{C}((t_1),..(t_n …
- 1,397
1
vote
1
answer
237
views
Cohomological dimension of transcendental p-adic extensions
Let $q$ denote a quadratic form over a field $k$.
The u-invariant of a field $u(k)$ is defined by $u(k):=\{ max (\mathrm{rank}(q)) $ | $ q $ is anisotropic over $k\}$.
Let $k = \mathbb{Q}_p$ for any …
- 1,397
1
vote
1
answer
144
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Dimension of binary motives of a quadric
Let $Q$ be a anisotropic quadric of dimension $d$ over $k$.
We work in the category of effective Chow-Motives over $k$.
Let $T$ be the Tate-Motive.
For a motive $M$ we write $M(l)$ for its $l$-th Tate …
- 1,397
0
votes
1
answer
139
views
Rost Correspondence and minimal Pfister-Neighbors
In http://www.math.uiuc.edu/K-theory/0357/ Karpenko utters the following:
Conjecture 1.6. If an anisotropic quadric $X = Q$ possesses a Rost correspondence,
then the quadratic form (defining $X$ …
- 1,397
5
votes
1
answer
221
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Rank four quadratic Form with non trivial discriminant in I(k)
Im sure this is a beginners question.
Let $k$ be a field and $I(k)$ the fundamental ideal in the Witt-ring W(k).
The Arason-Pfister-Hauptsatz states:
"If $\varphi$ is any anisotropic class in $I^n …
- 1,397
1
vote
1
answer
309
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Constructing groups of Type E^{66}_{7,1} having non trivial Tits algebra
This can be considered as a continuation of my last useful question:
Constructing groups of Type E7 with certain Tits Index
It is known that a quadratic form $q$ of dimension $12$, having splitting …
- 1,397
1
vote
0
answers
77
views
The splitting pattern of the Killing form of an algebraic group and the Tits index
Let us assume that $G$ is an anisotropic semisimple, connected algebraic group over a field $k$ of characteristic zero.
Let $K_G$ denote the class of its Killing form in the Witt ring of $k$.
Let $X$ …
- 1,397
4
votes
0
answers
155
views
Quadrics contained in the (complex) Cayley plane
In the paper
Ilev, Manivel - The Chow ring of the Cayley plane
we can learn, that $CH^8(X)$, with $X := E_6/P_1$, denoting the Cayley plane, has three generators with one of them being the class of …
- 1,397
4
votes
0
answers
117
views
Norm variety for n=5, p=2 not isomorphic to a quadric
In the paper "Motivic construction of cohomological invariants", the author displays a list of known norm varieties for several $n,p$ on page $11$. For $p=2, n=5$ it says that a norm variety is given …
- 1,397
5
votes
1
answer
406
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Constructing groups of Type E7 with certain Tits Index
In a new survey on $E_8$, namely
Skip Garibaldi - E8 the most exceptional group
, the author gives an example (Example 8.4., page 15) on how to construct a group of type E8 with a prescribed Tits-I …
- 1,397