On non-commutative twisting in étale and motivic cohomology

Jens Hornbostel[1]; Guido Kings

  • [1] Universität Regensburg NWF I, Mathematik 93040 Regensburg (Germany)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 4, page 1257-1279
  • ISSN: 0373-0956

Abstract

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This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups H 1 ( 𝒪 K [ 1 / S ] , H i ( X ¯ , ℚ p ( j ) ) ) , where X → Spec 𝒪 K [ 1 / S ] is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to H i ( X ¯ , ℤ p ( j ) ) . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.

How to cite

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Hornbostel, Jens, and Kings, Guido. "On non-commutative twisting in étale and motivic cohomology." Annales de l’institut Fourier 56.4 (2006): 1257-1279. <http://eudml.org/doc/10172>.

@article{Hornbostel2006,
abstract = {This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups $H^1(\mathcal\{O\}_K[1/S],H^i(\overline\{X\},\mathbb\{Q\}_p(j)))$, where $X\rightarrow \operatorname\{Spec\}\mathcal\{O\}_K[1/S]$ is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to $H^i(\overline\{X\},\mathbb\{Z\}_p(j))$. Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.},
affiliation = {Universität Regensburg NWF I, Mathematik 93040 Regensburg (Germany)},
author = {Hornbostel, Jens, Kings, Guido},
journal = {Annales de l’institut Fourier},
keywords = {Étale cohomology; motivic cohomology; non-commutative Iwasawa-theory; étale cohomology},
language = {eng},
number = {4},
pages = {1257-1279},
publisher = {Association des Annales de l’institut Fourier},
title = {On non-commutative twisting in étale and motivic cohomology},
url = {http://eudml.org/doc/10172},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Hornbostel, Jens
AU - Kings, Guido
TI - On non-commutative twisting in étale and motivic cohomology
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 4
SP - 1257
EP - 1279
AB - This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups $H^1(\mathcal{O}_K[1/S],H^i(\overline{X},\mathbb{Q}_p(j)))$, where $X\rightarrow \operatorname{Spec}\mathcal{O}_K[1/S]$ is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to $H^i(\overline{X},\mathbb{Z}_p(j))$. Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.
LA - eng
KW - Étale cohomology; motivic cohomology; non-commutative Iwasawa-theory; étale cohomology
UR - http://eudml.org/doc/10172
ER -

References

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