Modular Curves, Modular Surfaces, and Modular Fourfolds

dc.creatorRamakrishnan, Dinakar
dc.date2006-09-16
dc.date.accessioned2026-07-07T07:24:53Z
dc.date.available2026-07-07T07:24:53Z
dc.descriptionThis article surveys some recent work of the author on Hilbert modular fourfolds X. After some preliminaries on the cohomology and special, codimension 2 cycles Z on X of Hirzebruch-Zagier type, a proof of the Tate conjecture for X over abelian fields is exposed. It is followed by a description of a method to construct classes in the Bloch's Chow group CH^3(X,1) by using Hecke translates of the cycles Z as above with suitable intersections in translates of modular curves. The article ends with the introduction of a modular Gersten complex for a general Shimura variety X and the corresponding groups CH^p_{mod}(X) and CH^p_{mod}(X,1).
dc.description15 pages, Proceedings of a conference on Algebraic Cycles and Motives (in honor of Jacob Murre) in Leiden, The Netherlands
dc.identifierhttps://arxiv.org/abs/math/0609459
dc.identifierhttp://arxiv.org/abs/math/0609459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116539
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11F41; 11G35; 14C25; 14C35; 14J35
dc.titleModular Curves, Modular Surfaces, and Modular Fourfolds
dc.typetext

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