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math.NT2026
Computing residual representations of abelian threefolds with imaginary multiplication
Shiva Chidambaram, Pip Goodman
Let be an imaginary quadratic field. Let be a polarised abelian threefold defined over with geometric endomorphism algebra isomorphic to . We study residual Galois r…
math.NT2026
Point counts of abelian varieties over finite fields determining their zeta function
Shiva Chidambaram, Timo Keller
Let be an abelian variety of dimension over a finite field . We show that if is sufficiently large relative to , the point counts $\#A(\mathbf{F}_{…
math.NT2026
On the Visibility category of the Shafarevich--Tate group
Barinder S. Banwait, Jerson Caro, Shiva Chidambaram
Given an elliptic curve over $\Q$ and a nontrivial element of its Shafarevich--Tate group $\Sha(E)$, we introduce the \textbf{Visualization category} $\V(E; σ)$ of abelian…