2020 Fiscal Year Annual Research Report
Ｇジップを用いた志村多様体の幾何と法ｐ保型形式の研究
| Project/Area Number |
18F18311
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| Research Institution | Saitama University |
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| Co-Investigator(Kenkyū-buntansha) |
Koskivirta Jean・Stefan 埼玉大学, 理工学研究科, 助教 (00897613)
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| Project Period (FY) |
2018-11-09 – 2021-03-31
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| Keywords | 志村多様体 / Gジップのスタック / 法p保型形式 |
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| Outline of Annual Research Achievements |
I conducted research in the field of Number theory and algebraic geometry. In particular, I studied the space of global sections of automorphic vector bundles on the stack of G-zips of Pink-Wedhorn-Ziegler. In a joint paper with Naoki Imai, we determined this space for a general reductive group in terms of the Brylinski-Kostant filtration. This paper was published in Forum of Mathematics, Sigma in April 2021. I also started several related projects with Imai and Goldring that will be submitted this month for publication. One project is related to the construction of partial Hasse invariants, the other has to do with understanding which weights admit nonzero automorphic forms in characteristic p. Specifically, we construct automorphic forms in characteristic p whose vanishing locus is a given codimension one stratum in the flag space of a Shimura variety. We show that this form always exists and lies in the subvector bundles attached to the socle of the representation. In the second project, we prove several results regarding the zip cone, that was introduced in a previous paper. In particular, we show that if a certain explicit condition on the Galois action is satisfied, then the zip cone is spanned over the positive rationals by the weights of partial Hasse invariants (constructed in the first paper). I presented my research at several institutions.
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| Research Progress Status |
令和2年度が最終年度であるため、記入しない。
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| 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。
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