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tagged as open problem + small typo fixes
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jmc
jmc
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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 $X$) is a minimal Pfister neighbor.

Conjecture 1.6. If an anisotropic quadric $X = Q$ possesses a Rost correspondence, then the quadratic form (defining $X$) is a minimal Pfister neighbor.

Since the Paper has been released 15 years ago, iI wonder if there has been made any progress on the conjecture.

Everything regarding Rost-Projectors is defined within the paper.

I am quite new to the subject and iI am "working" myself through most of the papers in order of their release,so so it might be that my question is obsolete today. On the other hand, there is also a remark in "Rost Projectors and Steenrod Operations" by Karpenko and Merkurjev from 2002 that the problem is still not solved, except for the cases of $dim(X) = 3,7$.

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 $X$) is a minimal Pfister neighbor.

Since the Paper has been released 15 years ago, i wonder if there has been made any progress on the conjecture.

Everything regarding Rost-Projectors is defined within the paper.

I am quite new to the subject and i am "working" myself through most of the papers in order of their release,so it might be that my question is obsolete today. On the other hand, there is also a remark in "Rost Projectors and Steenrod Operations" by Karpenko and Merkurjev from 2002 that the problem is still not solved, except for the cases of $dim(X) = 3,7$.

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 $X$) is a minimal Pfister neighbor.

Since the Paper has been released 15 years ago, I wonder if there has been made any progress on the conjecture.

Everything regarding Rost-Projectors is defined within the paper.

I am quite new to the subject and I am "working" myself through most of the papers in order of their release, so it might be that my question is obsolete today. On the other hand, there is also a remark in "Rost Projectors and Steenrod Operations" by Karpenko and Merkurjev from 2002 that the problem is still not solved, except for the cases of $dim(X) = 3,7$.

tagged as open problem
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edit approved Mar 25, 2015 at 12:55
Konrad Voelkel
edit approved Mar 25, 2015 at 12:55
Konrad Voelkel
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nxir
nxir
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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 $X$) is a minimal Pfister neighbor.

Since the Paper has been released 15 years ago, i wonder if there has been made any progress on the conjecture.

Everything regarding Rost-Projectors is defined within the paper.

I am quite new to the subject and i am "working" myself through most of the papers in order of their release,so it might be that my question is obsolete today. On the other hand, there is also a remark in "Rost Projectors and Steenrod Operations" by Karpenko and Merkurjev from 2002 that the problem is still not solved, except for the cases of $dim(X) = 3,7$.