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過去の記録 ～06/10｜次回の予定｜今後の予定 06/11～
| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
次回の予定
2025年06月11日(水)
17:00-18:00 数理科学研究科棟(駒場) 117号室
Bruno Kahn 氏 (FJ-LMI)
Zeta and $L$-functions of Voevodsky motives
https://webusers.imj-prg.fr/~bruno.kahn/
Bruno Kahn 氏 (FJ-LMI)
Zeta and $L$-functions of Voevodsky motives
[ 講演概要 ]
We associate an $L$-function $L^{\text{near}}(M,s)$ to any geometric motive over a global field $K$ in the sense of Voevodsky. This is a Dirichlet series which converges in some half-plane and has an Euler product factorisation. When $M$ is the dual of $M(X)$ for $X$ a smooth projective variety, $L^{\text{near}}(M,s)$ differs from the alternating product of the zeta functions defined by Serre in 1969 only at places of bad reduction; in exchange, it is multiplicative with respect to exact triangles. If $K$ is a function field over $\mathbb{F}_q$, $L^{\text{near}}(M,s)$ is a rational function in $q^{-s}$ and enjoys a functional equation. The techniques use the full force of Ayoub's six (and even seven) operations.
[ 参考URL ]We associate an $L$-function $L^{\text{near}}(M,s)$ to any geometric motive over a global field $K$ in the sense of Voevodsky. This is a Dirichlet series which converges in some half-plane and has an Euler product factorisation. When $M$ is the dual of $M(X)$ for $X$ a smooth projective variety, $L^{\text{near}}(M,s)$ differs from the alternating product of the zeta functions defined by Serre in 1969 only at places of bad reduction; in exchange, it is multiplicative with respect to exact triangles. If $K$ is a function field over $\mathbb{F}_q$, $L^{\text{near}}(M,s)$ is a rational function in $q^{-s}$ and enjoys a functional equation. The techniques use the full force of Ayoub's six (and even seven) operations.
https://webusers.imj-prg.fr/~bruno.kahn/
