Timeline for On what varieties are the conjectures on $L$-functions true
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| Mar 31, 2018 at 14:07 | comment | added | François Brunault | For your question 1, see Nekovar's survey paper (1.4) or Deligne "Valeurs de fonctions $L$ et périodes d'intégrales" 5.2. The Euler factor at an archimedean place $v$ depends only on the Hodge structure $H^i(M_v)$. For your question 2, basically the only way to prove meromorphic continuation is to prove some kind of modularity for your variety $Y$. As an example, potential automorphy has recently been proved for abelian surfaces over totally real fields, which is sufficient to imply the first part of condition 2. | |
| Mar 31, 2018 at 9:45 | history | asked | Wenzhe | CC BY-SA 3.0 |