Year: 2019
Type: article
Abstract: We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks $$\mathop {G\hbox {-}{} \mathtt{Zip}}\nolimits ^{\mu }$$ . Restricting to zip data of Hodge type, we obtain a group-theoretical Hasse invariant on every Ekedahl–Oort stratum closure of a general Hodge-type Shimura variety. A key tool is the construction of a stack of zip flags $$\mathop {G\hbox {-}{} \mathtt{ZipFlag}}\nolimits ^\mu $$ , fibered in flag varieties over $$\mathop {G\hbox {-}{} \mathtt{Zip}}\nolimits ^{\mu }$$ . It provides a simultaneous generalization of the “classical case” homogeneous complex manifolds studied by Griffiths–Schmid and the “flag space” for Siegel varieties studied by Ekedahl–van der Geer. Four applications are obtained: (1) Pseudo-representations are attached to the coherent cohomology of Hodge-type Shimura varieties modulo a prime power. (2) Galois representations are associated to many automorphic representations with non-degenerate limit of discrete series Archimedean component. (3) It is shown that all Ekedahl–Oort strata in the minimal compactification of a Hodge-type Shimura variety are affine, thereby proving a conjecture of Oort. (4) Part of Serre’s letter to Tate on mod p modular forms is generalized to general Hodge-type Shimura varieties.
Source: Inventiones mathematicae
Authors: Wushi Goldring, Jean-Stefan Koskivirta
Institutions: Stockholm University, The University of Tokyo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,140
Award: 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
OpenAlex ID: W910231098