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Construction of torsion cohomology classes for KHT Shimura varieties
- Publication Year :
- 2019
-
Abstract
- Let $Sh_K(G,\mu)$ be a Shimura variety of KHT type, as introduced in Harris-Taylor book, associated to some similitude group $G/\mathbb Q$ and a open compact subgroup $K$ of $G(\mathbb A)$. For any irreducible algebraic $\overline{\mathbb Q}_l$-representation $\xi$ of $G$, let $V_\xi$ be the $\mathbb Z_l$-local system on $Sh_K(G,\mu)$. From my paper about p-stabilization, we know that if we allow the local component $K_l$ of $K$ to be small enough, then there must exists some non trivial cohomology classes with coefficient in $V_\xi$. The aim of this paper is then to construct explicitly such torsion classes with the control of $K_l$. As an application we obtain the construction of some new automorphic congruences between tempered and non tempered automorphic representations of the same weight and same level at $l$.
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1903.11000
- Document Type :
- Working Paper