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Chow Künneth decomposition for étale motives

Ivan Rosas-Soto

Abstract

In the present article we define an integral analogue of Chow-Künneth decomposition for étale motives. By using families of conservative functors we are able to establish a decomposition of the étale motive of commutative group schemes over a base and we relate to an integral étale Chow-Künneth decomposition of abelian varieties. For a projective variety $X$ of dimension $d$ over an algebraically closed field, we construct integral sub-motives $h^1_{\text{ét}}(X)$ and $h^{2d-1}_{\text{ét}}(X)$ of the motive $h_{\text{ét}}(X)$.

Chow Künneth decomposition for étale motives

Abstract

In the present article we define an integral analogue of Chow-Künneth decomposition for étale motives. By using families of conservative functors we are able to establish a decomposition of the étale motive of commutative group schemes over a base and we relate to an integral étale Chow-Künneth decomposition of abelian varieties. For a projective variety of dimension over an algebraically closed field, we construct integral sub-motives and of the motive .
Paper Structure (6 sections, 33 theorems, 92 equations)

This paper contains 6 sections, 33 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Étale decomposition
  4. Improved Manin version for the étale case
  5. Decomposition of abelian varieties
  6. Lg-actions on Lg

Key Result

Theorem 1

Let $k$ be an algebraically closed field and $G/k$ a connected commutative group scheme. Then the morphism is an isomorphism in $\text{DM}_\text{\'et}(k,\mathbb{Z})$.

Theorems & Definitions (76)

  • Theorem 1: Proposition \ref{['teoprin']}
  • Lemma : Lemma \ref{['consCD']}
  • Theorem 2: Theorem \ref{['relat']}
  • Theorem 3: Theorem \ref{['prodJac']}
  • Theorem 4
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Lemma 2.5
  • ...and 66 more