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代数学コロキウム
過去の記録 ～07/02｜次回の予定｜今後の予定 07/03～
| 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 |
今後の予定
2026年07月08日(水)
17:00-18:00 数理科学研究科棟(駒場) 117号室
Vova Sosnilo 氏 (理化学研究所 数理創造研究センター)
Descent for algebraic K-theory of algebraic stacks
https://vova-sosnilo.com/
Vova Sosnilo 氏 (理化学研究所 数理創造研究センター)
Descent for algebraic K-theory of algebraic stacks
[ 講演概要 ]
Algebraic K-theory satisfies descent with respect to Nisnevich covers, which allows one to deduce global computations for schemes to the affine case. For algebraic stacks this is insufficient, since algebraic stacks with nontrivial stabilizers do not admit Nisnevich covers by affine schemes. However, a theorem of Deshmukh shows that any algebraic stack with separated diagonal admits a Nisnevich surjection from an affine scheme. The Atiyah—Segal completion theorem measures precisely the failure of algebraic K-theory to satisfy descent with respect to Nisnevich surjections. We show that it holds for ANS algebraic stacks of finite type over a field of characteristic 0 using trace methods and equivariant resolution of singularities. Time permitting, we discuss an ongoing work attempting to extend this result in characteristic p.
[ 参考URL ]Algebraic K-theory satisfies descent with respect to Nisnevich covers, which allows one to deduce global computations for schemes to the affine case. For algebraic stacks this is insufficient, since algebraic stacks with nontrivial stabilizers do not admit Nisnevich covers by affine schemes. However, a theorem of Deshmukh shows that any algebraic stack with separated diagonal admits a Nisnevich surjection from an affine scheme. The Atiyah—Segal completion theorem measures precisely the failure of algebraic K-theory to satisfy descent with respect to Nisnevich surjections. We show that it holds for ANS algebraic stacks of finite type over a field of characteristic 0 using trace methods and equivariant resolution of singularities. Time permitting, we discuss an ongoing work attempting to extend this result in characteristic p.
https://vova-sosnilo.com/
