Supersingular curves on Picard modular surfaces modulo an inert prime

Ehud de Shalit; Eyal Goren

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arXiv · 1607.04170

Supersingular curves on Picard modular surfaces modulo an inert prime

Ehud de Shalit·Eyal Goren

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Abstract

We study the supersingular curves on Picard modular surfaces modulo a prime $p$ which is inert in the underlying quadratic imaginary field. We analyze the automorphic vector bundles in characteristic $p$, and as an application derive a formula relating the number of irreducible components in the supersingular locus to the second Chern class of the surface.

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Ehud de Shalit, Eyal Goren. 2016-07-14. Supersingular curves on Picard modular surfaces modulo an inert prime. https://arxiv.org/abs/1607.04170

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