3 problems

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Köhler–Roessler relative equivariant fixed-point formula conjecture
Relative fixed-point formula conjecture. The diagram
Conjectureopenarithmetic-geometry equivariant-k-theory fixed-point-formulasarXiv posted 2 days ago
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Köhler–Roessler rationality conjecture for equivariant analytic torsion
Let $M$ be an $S^{1}$ -equivariant projective complex manifold equipped with an $S^{1}$ -invariant Kähler metric, and let $E$ be an $S^{1}$ -equivariant complex vector bundle equipped…
Conjectureopenarithmetic-geometry equivariant-analytic-torsion fixed-point-formulasarXiv posted 2 days ago
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The Atiyah–Bott equivariant Lefschetz fixed-point formula
Atiyah–Bott conjecture. The $G$ -equivariant index of an elliptic operator can be computed purely in terms of data around the $G$ -fixed points.
Conjecturesolvedequivariant-index fixed-point-formulas representation-theoryarXiv posted 2 days ago

Köhler–Roessler relative equivariant fixed-point formula conjecture