All Questions
7 questions
1
vote
0
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90
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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 $X$ ...
- 12.9k
12
votes
1
answer
529
views
Quadrics in the Grothendieck ring
Let $\mathcal{Q}$ be an irreducible quadric in $\mathbb{P}^n(k)$, with $n \geq 2$ and $k$ a finite field. Let $K_0(V_k)$ be the Grothendieck ring of $k$-varieties. It is well known (it appears) that ...
- 4,111
4
votes
0
answers
161
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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 ...
- 17.4k
5
votes
1
answer
450
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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-...
- 1,479
4
votes
0
answers
121
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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 ...
- 17.6k
0
votes
1
answer
149
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 $X$) ...
- 5,504
1
vote
1
answer
155
views
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-...
- 17.4k