Relative Lie algebra cohomology of SU(2,1) and Eisenstein classes on Picard surfaces

2024/02/01 by Jitendra Bajpai, Bajpai, Jitendra, Mattia Cavicchi +1
Arts and Humanities · Mathematics · #11F70 #14D07 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Primary:11G40 #Representation Theory (math.RT) #Secondary:11F75

paper · pdf · doi:10.48550/arxiv.2402.00757

openalex publication_date 2024/02/01 · openalex created_date 2024/02/03 · openalex updated_date 2026/07/28

Abstract

We consider Picard surfaces, locally symmetric varieties S_Γ attached to the Lie group SU(2,1), and we construct explicit differential forms on S_Γ representing Eisenstein classes, i.e. cohomology classes restricting non-trivially to the boundary of the Borel-Serre compactification. This is needed for the computation of the class of the extensions of the Hodge structure that we have constructed in [2] according to the predictions of the Bloch-Beilinson conjectures. The tool for the construction of the differential forms is an analysis of relative Lie algebra cohomology of the principal series of SU(2,1) using recent methods of Buttcane and Miller.

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