Anticyclotomic diagonal cycle classes are shown to match Beilinson-Flach elements up to explicit factors for a CM weight-one Eisenstein degeneration.
Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits
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abstract
We consider the $\zeta$-regularized determinant of the Friedrichs extension of the Dirichlet Laplace-Beltrami operator on curvilinear polygonal domains with corners of arbitrary positive angles. In particular, this includes slit domains. We obtain a short time asymptotic expansion of the heat trace using a classical patchwork method. This allows us to define the $\zeta$-regularized determinant of the Laplacian and prove a comparison formula of Polyakov-Alvarez type for a smooth and conformal change of metric.
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Anticyclotomic diagonal classes and Beilinson--Flach elements
Anticyclotomic diagonal cycle classes are shown to match Beilinson-Flach elements up to explicit factors for a CM weight-one Eisenstein degeneration.