An Euler system for GU(2, 1)
David Loeffler, Christopher Skinner, Sarah Livia Zerbes
Abstract
Abstract We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of $${{\,\mathrm{GL}\,}}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mspace/> <mml:mi>GL</mml:mi> <mml:mspace/> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:math> over imaginary quadratic fields, using the cohomology of Shimura varieties for $${\text {GU}}(2, 1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>GU</mml:mtext> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> .
Topics & Concepts
MathematicsEuler systemPure mathematicsEuler's formulaAutomorphic formCohomologyQuadratic fieldAlgebraic numberQuadratic equationThe ImaginaryAlgebra over a fieldMathematical analysisEuler equationsGeometryQuadratic functionPsychotherapistPsychologyAdvanced Algebra and GeometryAlgebraic Geometry and Number TheoryGeometry and complex manifolds