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代数学コロキウム
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 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 |
2022年07月06日(水)
17:00-18:00 ハイブリッド開催
数理科学研究科所属以外の方は、オンラインでのご参加をお願いいたします。
劉 沛江 氏 (東京大学大学院数理科学研究科)
The characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves (ENGLISH)
数理科学研究科所属以外の方は、オンラインでのご参加をお願いいたします。
劉 沛江 氏 (東京大学大学院数理科学研究科)
The characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves (ENGLISH)
[ 講演概要 ]
$\ell$-adic GKZ hypergeometric sheaves are defined to be étale analogues of GKZ hypergeometric $\mathcal{D}$-modules. We introduce an algorithm of computing the characteristic cycles of certain type of $\ell$-adic GKZ hypergeometric sheaves. We compute the irreducible components by a push-forward formula for characteristic cycles of étale sheaves, and compute the multiplicities by considering a comparison theorem between the characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves and those of non-confluent GKZ hypergeometric $\mathcal{D}$-modules. We also explain the limitation of our algorithm by an example.
$\ell$-adic GKZ hypergeometric sheaves are defined to be étale analogues of GKZ hypergeometric $\mathcal{D}$-modules. We introduce an algorithm of computing the characteristic cycles of certain type of $\ell$-adic GKZ hypergeometric sheaves. We compute the irreducible components by a push-forward formula for characteristic cycles of étale sheaves, and compute the multiplicities by considering a comparison theorem between the characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves and those of non-confluent GKZ hypergeometric $\mathcal{D}$-modules. We also explain the limitation of our algorithm by an example.
