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General Horizontal Norm Compatible Systems on unitary Shimura varieties
Reda Boumasmoud
The ultimate goal of the paper is to construct a novel norm-compatible family of cycles appearing in the context of Gross--Gan--Prasad cycles arising from Shimura varieties attache…
Seed Relations for Eichler--Shimura congruences and Euler systems
Reda Boumasmoud
This paper proves that the -operator attached to a cocharacter is a right root of the corresponding Hecke polynomial. This result is an important ingredient in the proo…
The ring of U-operators: Definitions and Integrality
Reda Boumasmoud
In this paper, we define and study the arithmetic of the ring of -operators for reductive -adic groups. These operators generalise the notion of "successor" operator…
A tale of parahoric--Hecke algebras, Bernstein and Satake homomorphisms
Reda Boumasmoud
Let be a connected reductive group over a {non-archimedean local field} . Let be the parahoric subgroup attached to a facet in the Bru…