arXiv subjects

Dac-Nhan-Tam Nguyen

Publications and source records attributed to Dac-Nhan-Tam Nguyen.

4 recordsLinked to original sources

arXiv2025

Congruent modular forms and anticyclotomic Iwasawa theory

Let $p$ be an odd prime. Consider normalized newforms $f_1,f_2$ that both satisfy the Heegner hypothesis for an imaginary quadratic field $K$ and suppose that they induce isomorphic residual Galois representations. In the work of Greenberg-Vatsal and Emerton-Pollack-Weston, the authors compare the cyclotomic Iwasawa $μ$ and $λ$-invariants of $f_1$ and $f_2$. We extend this to the anticyclotomic indefinite setting by comparing the BDP $p$-adic $L$-functions attached to $f_1$ and $f_2$. Using this comparison, we obtain arithmetic implications for both generalized Heegner cycles and the Iwasawa main conjecture.

math.NT↗

arXiv2025

Galois cohomology of elliptic curves over anticyclotomic extensions

Let $K$ be an imaginary quadratic field and $p$ be an odd prime number. Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. We study the Iwasawa theory of $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$ by adopting a unifying framework. We also study the Galois cohomology of the dual Selmer group of $E$ over the unique $\mathbb{Z}_p^2$-extension of $K$ as well as over the anticyclotomic extension of $K$.

math.NT↗

arXiv2025

On $λ$-invariants of congruent modular forms in the anticyclotomic, indefinite setting

We give a precise, computable formula for comparing $λ$-invariants between modular forms in the anticyclotomic indefinite setting where the Selmer groups have positive rank. This is an improvement of Hatley-Lei \cite{HL19, HL21} where the authors give a formula with incomputable error terms.

math.NT↗

arXiv2025

Congruent elliptic curves over some $p$-adic Lie extensions

Let $p$ be an odd prime number. In this article, we study the variation of Iwasawa invariants among $p$-congruent elliptic curves over certain $p$-adic Lie extensions. We investigate both the classical Selmer group as well as the fine Selmer group.

math.NT↗