Supersingular curves on Picard modular surfaces modulo an inert prime

详细信息    查看全文

• 作者：Ehud de Shalit^a ; ^{deshalit@math.huji.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Eyal Z. Goren^b ; ^{eyal.goren@mcgill.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Picard modular surface ; Supersingular locus ; Hasse invariant
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：171
• 期：Complete
• 页码：391-421
• 全文大小：536 K

文摘

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.