14 citations · 67 across the 20 of their papers we have counts for
4 papers · 2 filters
Serre-Tate theory for Shimura varieties of Hodge type
Ananth N. Shankar, Rong Zhou
We study the formal neighbourhood of a point in -ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a…
2-Selmer groups of hyperelliptic curves with two marked points
Ananth N. Shankar
We consider the family of hyperelliptic curves over $\Q$ of fixed genus along with a marked rational Weierstrass point and a marked rational non-Weierstrass point. When these curve…
The -curvature conjecture and monodromy about simple closed loops
Ananth N. Shankar
The Grothendieck-Katz -curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a vari…
Unlikely Intersections in Finite Characteristic
Ananth N Shankar, Jacob Tsimerman
We present a heuristic argument based on Honda-Tate theory against many conjectures in `unlikely intersections' over the algebraic closure of a finite field; notably, we conjecture…