TY - JOUR
T1 - The weight reduction of mod p Siegel modular forms for GSp4 and theta operators
AU - Yamauchi, Takuya
N1 - Funding Information:
The author is partially supported by JSPS KAKENHI Grant Number (B) No. 19H01778.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2023/1
Y1 - 2023/1
N2 - In this paper we investigate the (classical) weights of mod p Siegel modular forms of degree 2 toward studying Serre’s conjecture for GSp4/ Q. We first construct various theta operators on the space of such forms à la Katz and define the theta cycles for the specific theta operators. Secondly, we study the partial Hasse invariants on each Ekedahl–Oort stratum and their local behaviors. This enables us to obtain a kind of weight reduction theorem for mod p Siegel modular forms of degree 2 without increasing the level.
AB - In this paper we investigate the (classical) weights of mod p Siegel modular forms of degree 2 toward studying Serre’s conjecture for GSp4/ Q. We first construct various theta operators on the space of such forms à la Katz and define the theta cycles for the specific theta operators. Secondly, we study the partial Hasse invariants on each Ekedahl–Oort stratum and their local behaviors. This enables us to obtain a kind of weight reduction theorem for mod p Siegel modular forms of degree 2 without increasing the level.
KW - Galois representations
KW - Mod p Siegel modular forms
KW - Partial Hasse invariants
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U2 - 10.1007/s00209-022-03153-x
DO - 10.1007/s00209-022-03153-x
M3 - Article
AN - SCOPUS:85143490367
SN - 0025-5874
VL - 303
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1
M1 - 10
ER -