R. Pollack

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math.NT2025

On the maximality of the $I^»$ -invariants of Mazur--Tate elements

Antonio Lei, Robert Pollack, Naman Pratap

Let $E$ be an elliptic curve with good ordinary reduction at an odd prime $p$ . Assuming that Greenberg's $I^¼ = 0$ conjecture holds, we show that the $I^»$ -invariants of the Mazur--Tat…

math.NT2025

On the Iwasawa Invariants of Mazur--Tate elements of elliptic curves at additive primes

Antonio Lei, Robert Pollack, Naman Pratap

We investigate the $λ$ -invariants of Mazur--Tate elements of elliptic curves defined over the field of rational numbers at primes of additive reduction. We explain their growth and…

math.NT2025

The refined Tamagawa number conjectures for $GL_{2}$

Chan-Ho Kim, Robert Pollack

Let $f$ be a cuspidal newform and $p \geq 3$ a prime such that the associated $p$ -adic Galois representation has large image. We establish a new and refined "Birch and Swinnerton-D…

math.NT2024

Iwasawa invariants in residually reducible Hida families

Robert Pollack, Preston Wake

We study the variation of $I^¼$ -invariants of modular forms in a cuspidal Hida family in the case that the family intersects an Eisenstein family. We allow for intersections that oc…

On the maximality of the I^»-invariants of Mazur--Tate elements

On the Iwasawa Invariants of Mazur--Tate elements of elliptic curves at additive primes

The refined Tamagawa number conjectures for GL2​

Iwasawa invariants in residually reducible Hida families

On the maximality of the $I^»$ -invariants of Mazur--Tate elements

The refined Tamagawa number conjectures for $GL_{2}$