| Project/Area Number |
19F19022
|
|---|
| Research Category |
Grant-in-Aid for JSPS Fellows
|
| Allocation Type | Single-year Grants |
|---|
| Section | 外国 |
|---|
| Review Section |
Basic Section 11010:Algebra-related
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
今井 直毅 東京大学, 大学院数理科学研究科, 准教授 (90597775)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
GAISIN ILDAR 東京大学, 数理(科)学研究科(研究院), 外国人特別研究員
|
|---|
| Project Period (FY) |
2019-04-25 – 2021-03-31
|
| Project Status |
Completed (Fiscal Year 2020)
|
| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2020: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2019: ¥1,200,000 (Direct Cost: ¥1,200,000)
|
|---|
| Keywords | Cohomology |
|---|
| Outline of Research at the Start |
Fargues-Fontaine 曲線上において，ベクトル束とその付加構造のモジュライを考えることによって Deligne-Lusztig 多様体の類似を構成する．構成した空間やそのある意味でのコンパクト化を幾何的に調べ，そのコホモロジーに局所保型誘導を幾何学的に実現する．これによって，有限体上の代数群に対する Deligne-Lusztig 理論の局所体類似が構成される．
|
| Outline of Annual Research Achievements |
During the period April 2020-March 2021, together with my collegue Teruhisa Koshikawa, we developed a relative version of A_Inf-cohomology. First some background: Given a proper smooth formal scheme X over the ring of integers, Bhatt-Morrow-Scholze constructed a complex of A_Inf-modules which specializes to other p-adic cohomology theories (their work published in 2018). In recent work of Koshikawa and myself we generalize this construction to the relative situation. In
short, this means that for a smooth morphism of p-adic formal schemes f: X -> Y, we construct a complex (using the decalage functor) living on the pro-etale site of the adic generic fiber of Y, which interpolates the de Rham complex. Although, our methods are similar to that of Bhatt-Morrow-Scholze, there is the appearance of a new object in this setup: fibered product of topoi. One difference in this setup (compared to BMS) is that results are only possible up to almost ambiguity (due to almost non-zero elements in higher cohomology groups for the pro-etale topology). One consequence of our work is the existence of a relative Hodge-Tate spectral sequence which generalizes the ones constructed by Caraiani-Scholze (dvr setting) et Abbes-Gros (scheme setting). Moreover we compare our relative A_Inf-cohomology with the prismatic/q-crystalline theory developed by Bhatt-Scholze.
|
| Research Progress Status |
令和2年度が最終年度であるため、記入しない。
|
| Strategy for Future Research Activity |
令和2年度が最終年度であるため、記入しない。
|
