algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety equivariant arithmetic variety; fixed point scheme; Arakelov geometry; fixed point formula; Lefschetz-Riemann-Roch; equivariant analytic torsion; equivariant Quillen metric; Bott-Chern class; Chern character; Todd form; Bismut equivariant R-class; wave front set; Euler-Green current; Bismut's immersion theorem; deformation to the normal cone; equivariant arithmetic degree 