3 problems

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Simpson's integrality conjecture for rigid representations
Let $X$ be the variety under consideration. A representation $\rho:\pi_1(X)\to \mathrm{GL}_r(\mathbb{C})$ is integral if it is conjugate to a representation…
Conjecturesolvedarithmetic-geometry character-varieties rigid-local-systemsarXiv posted 2 days ago
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Simpson's geometricity conjecture for rigid representations
Let $X$ be the variety under consideration and let $\rho:\pi_1(X)\to \mathrm{GL}_r(\mathbb{C})$ be a rigid representation, meaning that its character-variety point is isolated. A r…
Conjecturesolvedarithmetic-geometry nonabelian-hodge-theory rigid-local-systemsarXiv posted 2 days ago
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Langlands correspondence conjecture for rigid automorphic data
Langlands correspondence conjecture for rigid objects. The local system $\mathcal{F}_{\pi}$ is cohomologically rigid. Moreover, if…
Conjectureopenautomorphic-representations langlands-correspondence rigid-local-systemsarXiv posted 2 days ago

Simpson's integrality conjecture for rigid representations