2023 Fiscal Year Annual Research Report
Arithmetic cohomology over local fields
| Project/Area Number |
18K03258
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| Research Institution | Rikkyo University |
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Principal Investigator |
ガイサ トーマス 立教大学, 理学部, 教授 (30571963)
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Keywords | Weil etale cohomology / Local class field theory |
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| Outline of Annual Research Achievements |
Due to corona there was a small delay in the project, and I used the remaining funds to finish up the research project with Baptiste Morin. This resulted in two publications, both of which have now appeared.
In the first paper we outline the definition of a Weil-etale cohomology theory for varieties over local fields which satisfy a Pontrjagin duality theory. The groups are objects of the heart of the t-structure on the derived category of locally compact abelian groups. We also prove a duality result in weight zeoro.
This paper has appeared in January 2024 in Journal of the Institute Math. Jussieu.
In the second paper we prove results on class field theory over local fields, generalizing and improving work of S.Saito and Yoshida. We give an integral model for the fundamental group, and some extra information on the kernel of the reciprocity map. This paper has appeared online, and will appear in print in July 2024 in the Journal of Number Theory.
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