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過去の記録 ～10/29｜次回の予定｜今後の予定 10/30～
| 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11月04日(火)
17:00-18:00 数理科学研究科棟(駒場) 117号室
岩佐亮明 氏 (University of Copenhagen)
Descent and pro-excision
岩佐亮明 氏 (University of Copenhagen)
Descent and pro-excision
[ 講演概要 ]
The theme of this talk is descent and excision of cohomology theories of schemes. We will start with a discussion of the canonical topology on spectral schemes. Unlike on classical schemes, this topology includes many other types of covers, such as h-covers. Then I will explain that THH and TC satisfy descent with respect to the canonical topology, which generalizes the flat descent by Bhatt—Morrow—Scholze. This in turn implies the cdh descent of K-theory on spectral schemes, despite its failure on classical schemes. Furthermore, this implies the cdh pro-excision of K-theory on spectral schemes, which generalizes the derived case by Kelly—Saito—Tamme (the original noetherian case is due to Kerz—Strunk—Tamme). Our proof of the cdh pro-excision is quite different from the previous ones and is more algebraic in nature. The results presented here are based on discussions with Antieau, Burklund, and Krause.
The theme of this talk is descent and excision of cohomology theories of schemes. We will start with a discussion of the canonical topology on spectral schemes. Unlike on classical schemes, this topology includes many other types of covers, such as h-covers. Then I will explain that THH and TC satisfy descent with respect to the canonical topology, which generalizes the flat descent by Bhatt—Morrow—Scholze. This in turn implies the cdh descent of K-theory on spectral schemes, despite its failure on classical schemes. Furthermore, this implies the cdh pro-excision of K-theory on spectral schemes, which generalizes the derived case by Kelly—Saito—Tamme (the original noetherian case is due to Kerz—Strunk—Tamme). Our proof of the cdh pro-excision is quite different from the previous ones and is more algebraic in nature. The results presented here are based on discussions with Antieau, Burklund, and Krause.
