Projective Completion of Moduli of $t$-Connections on Curves in Positive and Mixed Characteristic

Mark Andrea A. de Cataldo; Siqing Zhang

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arXiv · 2104.12209

Projective Completion of Moduli of $t$-Connections on Curves in Positive and Mixed Characteristic

Mark Andrea A. de Cataldo·Siqing Zhang

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Abstract

We generalize a compactification technique due to C. Simpson in the context of $\mathbb{G}_m$-actions over the ground field of complex numbers, to the case of a universally Japanese base ring. We complement this generalized compactification technique so that it can sometimes yield projectivity results for these compactifications. We apply these projectivity results to the Hodge, de Rham, and Dolbeault moduli spaces for curves, with special regards to ground fields of positive characteristic.

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Mark Andrea A. de Cataldo, Siqing Zhang. 2021-04-25. Projective Completion of Moduli of $t$-Connections on Curves in Positive and Mixed Characteristic. https://arxiv.org/abs/2104.12209

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