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Elden Elmanto
Elden Elmanto
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I believe you can get results along these lines if you replace Zar with something called the $\ell$dh topology which is a modification of the cdh topology. This topology depends on $\ell$ which is a prime that is not equal to the characteristic you are working over and is a replacement for resolution of singularities over finite fields. The result is originally in Shane Kelly's PhD thesis: http://arxiv.org/abs/1305.5349

And this is a consequence of corollary 4.25 of http://arxiv.org/pdf/1305.5690v2.pdf which states that every $M\mathbb{Z}_{(\ell)}$-module spectrum satisfies $\ell$dh descent.

I believe you can get results along these lines if you replace Zar with something the $\ell$dh topology which is a modification of the cdh topology. This topology depends on $\ell$ which is a prime that is not equal to the characteristic you are working over and is a replacement for resolution of singularities over finite fields. The result is originally in Shane Kelly's PhD thesis: http://arxiv.org/abs/1305.5349

And this is a consequence of corollary 4.25 of http://arxiv.org/pdf/1305.5690v2.pdf which states that every $M\mathbb{Z}_{(\ell)}$-module spectrum satisfies $\ell$dh descent.

I believe you can get results along these lines if you replace Zar with something called the $\ell$dh topology which is a modification of the cdh topology. This topology depends on $\ell$ which is a prime that is not equal to the characteristic you are working over and is a replacement for resolution of singularities over finite fields. The result is originally in Shane Kelly's PhD thesis: http://arxiv.org/abs/1305.5349

And this is a consequence of corollary 4.25 of http://arxiv.org/pdf/1305.5690v2.pdf which states that every $M\mathbb{Z}_{(\ell)}$-module spectrum satisfies $\ell$dh descent.

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Elden Elmanto
Elden Elmanto
  • 2.3k
  • 1
  • 17
  • 33

I believe you can get results along these lines if you replace Zar with something the $\ell$dh topology which is a modification of the cdh topology. This topology depends on $\ell$ which is a prime that is not equal to the characteristic you are working over and is a replacement for resolution of singularities over finite fields. The result is originally in Shane Kelly's PhD thesis: http://arxiv.org/abs/1305.5349

And this is a consequence of corollary 4.25 of http://arxiv.org/pdf/1305.5690v2.pdf which states that every $M\mathbb{Z}_{(\ell)}$-module spectrum satisfies $\ell$dh descent.