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Number Theory Seminar
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2025/05/21
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Toni Annala (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
https://tannala.com/
Toni Annala (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
[ Abstract ]
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.
[ Reference 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/
