Développement fin de la contribution unipotente à la formule des traces sur un corps global de caractéristique p>0, I
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914636152963072 |
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| author | Lemaire, Bertrand |
| author_facet | Lemaire, Bertrand |
| contents | For a field $F$ and a connected reductive group $G$ defined over $F$, we develop a theory of Kempf-Rousseau-Hesselink unipotent $F$-strata in $G(F)$ that should allow us to attack open problems in positive characteristic. As an application, we use this theory to establish the fine expansion of the unipotent contribution to the (non-twisted) trace formula over a global field of characteristic $p>0$. The unipotent $F$-strata play here the role of the unipotent geometric orbits in Arthur's work over a number field. The expansion in terms of products of local distributions is not discussed here; it will be the subject of further work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03792 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Développement fin de la contribution unipotente à la formule des traces sur un corps global de caractéristique p>0, I Lemaire, Bertrand Representation Theory Number Theory 20G15, 14L24, 20G35, 11F72 For a field $F$ and a connected reductive group $G$ defined over $F$, we develop a theory of Kempf-Rousseau-Hesselink unipotent $F$-strata in $G(F)$ that should allow us to attack open problems in positive characteristic. As an application, we use this theory to establish the fine expansion of the unipotent contribution to the (non-twisted) trace formula over a global field of characteristic $p>0$. The unipotent $F$-strata play here the role of the unipotent geometric orbits in Arthur's work over a number field. The expansion in terms of products of local distributions is not discussed here; it will be the subject of further work. |
| title | Développement fin de la contribution unipotente à la formule des traces sur un corps global de caractéristique p>0, I |
| topic | Representation Theory Number Theory 20G15, 14L24, 20G35, 11F72 |
| url | https://arxiv.org/abs/2212.03792 |