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Number Theory Seminar
Seminar information archive ～07/02｜Next seminar｜Future seminars 07/03～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2026/07/08
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Vova Sosnilo (RIKEN iTHEMS)
Descent for algebraic K-theory of algebraic stacks
https://vova-sosnilo.com/
Vova Sosnilo (RIKEN iTHEMS)
Descent for algebraic K-theory of algebraic stacks
[ Abstract ]
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.
[ Reference 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/
