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Higgs bundles over good reduction of Shimura curve associated with quaternion division algebra

Mao Sheng, Jiajin Zhang, Kang Zuo

Number 30
Authors Jiajin Zhang
Mao Sheng
Kang Zuo
Year 2010

We study the Higgs bundles over good reduction of Shimura curve associated with quaternion division algebra to obtain some global results of Shimura curve in characteristic p. We obtain the mass formula counting the number of geometric points of the degeneracy locus in the Newton polygon stratification. Among the Higgs bundles over the Shimura curve in characteristic p, we find examples of semi-stable bundles which attain the upperbound of the instability under the Frobenius pull-back, as well as examples of strongly semi-stable bundles. We discuss the relation of the Higgs bundles with the recent advances in p-adic non-abelian Hodge theory. One sees in one example a comparison between the classical (complex) Simpson correspondence and the p-adic Simpson correspondence

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