Supersingular curves on Picard modular surfaces modulo an inert prime

Ehud de Shalit; Eyal Z. Goren

doi:10.1016/j.jnt.2016.07.001

Supersingular curves on Picard modular surfaces modulo an inert prime

Ehud de Shalit^*
, Eyal Z. Goren

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	391-421
Number of pages	31
Journal	Journal of Number Theory
Volume	171
DOIs	https://doi.org/10.1016/j.jnt.2016.07.001
State	Published - 1 Feb 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Hasse invariant
Picard modular surface
Supersingular locus

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10.1016/j.jnt.2016.07.001

Cite this

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title = "Supersingular curves on Picard modular surfaces modulo an inert prime",

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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AB - 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.

KW - Hasse invariant

KW - Picard modular surface

KW - Supersingular locus

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Supersingular curves on Picard modular surfaces modulo an inert prime

Abstract

Bibliographical note

Keywords

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