The ring of U-operators: Definitions and Integrality

Reda Boumasmoud

Published 2021-06-23Version 1

In this paper, we define and study the arithmetic of the ring of $\mathbb{U}$-operators. These operators generalize the notion of "successor" operators for trees with a marked end. We show that they are integral over the spherical Hecke algebra. This integrality intervene crucially in the construction of Euler systems obtained from special cycles of general Shimura varieties and in the generalization of the famous Eichler--Shimura relation.