A-upper motives of reductive groups
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929741903167488 |
|---|---|
| author | De Clercq, Charles Karpenko, Nikita Quéguiner-Mathieu, Anne |
| author_facet | De Clercq, Charles Karpenko, Nikita Quéguiner-Mathieu, Anne |
| contents | Given a prime number $p$, we perform the study of Chow motives and motivic decompositions, with coefficients in $\mathbb{Z}/p\mathbb{Z}$, of projective homogeneous varieties for $p'$-inner $p$-consistent reductive algebraic groups. Assorted with the known case of $p$-inner reductive groups, our results cover all absolutely simple groups of type not $^3\!D_4$ or $^6\!D_4$, among other examples. First, we define the A-upper motives of such a reductive group $G$; they are indecomposable motives, naturally related to Artin motives built out of spectra of subextensions of a minimal extension over which $G$ become of inner type. With this in hand, we carry on the qualitative study of motivic decompositions for projective $G$-homogeneous varieties. Providing geometric isomorphism criteria for A-upper motives, we obtain a classification of motives of projective $G$-homogeneous varieties, by means of their higher Artin-Tate traces. We also show that the higher Tits $p$-indexes of the group $G$ determine its motivic equivalence class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A-upper motives of reductive groups De Clercq, Charles Karpenko, Nikita Quéguiner-Mathieu, Anne Algebraic Geometry Given a prime number $p$, we perform the study of Chow motives and motivic decompositions, with coefficients in $\mathbb{Z}/p\mathbb{Z}$, of projective homogeneous varieties for $p'$-inner $p$-consistent reductive algebraic groups. Assorted with the known case of $p$-inner reductive groups, our results cover all absolutely simple groups of type not $^3\!D_4$ or $^6\!D_4$, among other examples. First, we define the A-upper motives of such a reductive group $G$; they are indecomposable motives, naturally related to Artin motives built out of spectra of subextensions of a minimal extension over which $G$ become of inner type. With this in hand, we carry on the qualitative study of motivic decompositions for projective $G$-homogeneous varieties. Providing geometric isomorphism criteria for A-upper motives, we obtain a classification of motives of projective $G$-homogeneous varieties, by means of their higher Artin-Tate traces. We also show that the higher Tits $p$-indexes of the group $G$ determine its motivic equivalence class. |
| title | A-upper motives of reductive groups |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.11030 |