ABELIANIZATION OF HIGGS BUNDLES FOR QUASI-SPLIT REAL GROUPS

We study the Hitchin map for Gℝ-Higgs bundles on a smooth curve, where Gℝ is quasi-split real form of complex reductive algebraic group G. By looking at moduli stack regular bundles, we prove that it induces banded gerbe structure slightly larger stack, whose band given by sheaves tori. This characterization yields cocyclic description fibres corresponding means cameral data. According to this, are categories principal torus cover. The points inside G-Higgs contained in substack fixed an involution induced Cartan Gℝ. determine this and stable correspondence with bundles.