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Finiteness of reductions of Hecke orbits
Mark Kisin, Yeuk Hay Joshua Lam, Ananth N. Shankar +1
We prove two finiteness results for reductions of Hecke orbits of abelian varieties over local fields: one in the case of supersingular reduction and one in the case of reductive m…
Families of elliptic curves ordered by conductor
Ananth N. Shankar, Arul Shankar, Xiaoheng Wang
In this article, we study the family of elliptic curves , having good reduction at and , and whose -invariants are small. Within this set of elliptic curves…
Almost ordinary abelian varieties over finite fields
Abhishek Oswal, Ananth N. Shankar
We provide a characterization of almost ordinary abelian varieties over finite fields, and use this characterization to provide lower bounds for the sizes of some almost ordinary i…
Reductions of abelian surfaces over global function fields
Davesh Maulik, Ananth N. Shankar, Yunqing Tang
Let be a non-isotrivial ordinary abelian surface over a global function field with good reduction everywhere. Suppose that does not have real multiplication by any real qua…
The rank two -curvature conjecture on generic curves
Anand Patel, Ananth N. Shankar, Junho Peter Whang
We prove the -curvature conjecture for rank two vector bundles with connection on generic curves, by combining deformation techniques for families of varieties and topological a…