Hitchin fibration and endoscopy (Q2491163)

The Hitchin fibration is a tool to investigate moduli-spaces of \(G\)-bundles (\(G\) a reductive group) on a curve. Its total space is fibred in two ways: Once over the moduli space of bundles and once over the space of conjugacy classes of sections of the adjoint bundle. For sufficiently generic conjugacy classes (called ``elliptic'') the paper translates geometric data into the language of orbital integrals and endoscopic groups. This allows to proof certain purity statements. Some of the proofs appear a little bit hasty but this does not affect the correctness of the results.