本文印刷
全画面プリント
代数学コロキウム
過去の記録 ～05/20｜次回の予定｜今後の予定 05/21～
| 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05月21日(水)
17:00-18:00 数理科学研究科棟(駒場) 117号室
Toni Annala 氏 (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
https://tannala.com/
Toni Annala 氏 (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
[ 講演概要 ]
In recent joint work with Hoyois and Iwasa, we discovered that non-A¹-invariant motivic homotopy theory offers a new lens for understanding logarithmic cohomology theories. Central to this perspective is A¹-colocalization, which produces a cohomology theory whose value on a smooth scheme U agrees with the "logarithmic cohomology" of a good compactification (X,D). In many examples, including de Rham and crystalline cohomology, the quotation marks can be dropped, as A¹-colocalization recovers the classical logarithmic cohomology groups. I will explain this connection and, time permitting, sketch a proof of the duality theorem underlying this phenomenon, which states that smooth projective schemes have a dualizable motive.
[ 参考URL ]In recent joint work with Hoyois and Iwasa, we discovered that non-A¹-invariant motivic homotopy theory offers a new lens for understanding logarithmic cohomology theories. Central to this perspective is A¹-colocalization, which produces a cohomology theory whose value on a smooth scheme U agrees with the "logarithmic cohomology" of a good compactification (X,D). In many examples, including de Rham and crystalline cohomology, the quotation marks can be dropped, as A¹-colocalization recovers the classical logarithmic cohomology groups. I will explain this connection and, time permitting, sketch a proof of the duality theorem underlying this phenomenon, which states that smooth projective schemes have a dualizable motive.
https://tannala.com/
