Higgs bundles over the good reduction of a quaternionic Shimura curve
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Mao Sheng
,
Jiajin Zhang
Abstract
This paper is devoted to the study of the Higgs bundle associated with the universal abelian variety over the good reduction of a Shimura curve of PEL type. Due to the endomorphism structure, the Higgs bundle decomposes into the direct sum of Higgs subbundles of rank two. They are basically divided into two types: uniformizing type and unitary type. As the first application we obtain the mass formula counting the number of geometric points of the degeneracy locus in the Newton polygon stratification. We show that each Higgs subbundle is Higgs semistable. Furthermore, for each Higgs subbundle of unitary type, either it is strongly semistable, or its Frobenius pull-back of a suitable power achieves the upper bound of the instability. We describe the Simpson–Ogus–Vologodsky correspondence for the Higgs subbundles in terms of the classical Cartier descent.
©[2012] by Walter de Gruyter Berlin Boston
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- Conformal maps from a 2-torus to the 4-sphere
- Sofic random processes
- Overlap properties of geometric expanders
- Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8
- A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
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Artikel in diesem Heft
- Conformal maps from a 2-torus to the 4-sphere
- Sofic random processes
- Overlap properties of geometric expanders
- Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8
- A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
- Spin representations of Weyl groups and the Springer correspondence
- Higgs bundles over the good reduction of a quaternionic Shimura curve
