Geodesic
Mod $p$ local-global compatibility for $\operatorname{GSp}_{4}(\mathbb{Q}_{p})$ in the ordinary case
Documenta mathematica, Tome 29 (2024) no. 4, pp. 863-919

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Let F be a totally real field of even degree in which p splits completely. Let rˉ:GF​→GSp4​(Fp​) be a modular Galois representation unramified at all finite places away from p and upper-triangular, maximally nonsplit, and of parallel weight at places dividing p. Fix a place w dividing p. Assuming certain genericity conditions and Taylor–Wiles assumptions, we prove that the GSp4​(Fw​)-action on the corresponding Hecke-isotypic part of the space of mod p automorphic forms on a compact mod center form of GSp4​ with infinite level at w determines rˉ∣GFw​​​.
DOI : 10.4171/dm/960
Classification : 11F80, 11F33
Mots-clés : algebraic automorphic forms, Galois representations 
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John Enns; Heejong Lee. Mod $p$ local-global compatibility for $\operatorname{GSp}_{4}(\mathbb{Q}_{p})$ in the ordinary case. Documenta mathematica, Tome 29 (2024) no. 4, pp. 863-919. doi: 10.4171/dm/960

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