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

2 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	American 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.",

keywords = "Hasse invariant, Picard modular surface, Supersingular locus",

author = "{de Shalit}, Ehud and Goren, {Eyal Z.}",

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year = "2017",

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doi = "10.1016/j.jnt.2016.07.001",

language = "American English",

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AU - de Shalit, Ehud

AU - Goren, Eyal Z.

PY - 2017/2/1

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N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84991512287&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2016.07.001

DO - 10.1016/j.jnt.2016.07.001

M3 - Article

AN - SCOPUS:84991512287

SN - 0022-314X

VL - 171

SP - 391

EP - 421

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Supersingular curves on Picard modular surfaces modulo an inert prime

Abstract

Bibliographical note

Keywords

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