H. Laxmi

activity

20222026

collaborators

6 papers

math.AG2026

Combs and complex structures on the six-sphere

Jeff Viaclovsky

We construct complex structures on the six-sphere $S^{6}$ with arbitrarily large local Kuranishi dimension. As a corollary, we find the same phenomenon holds for the smooth manifold…

math.NT2025

Stability of 2-class groups in the $Z_{2}$ -extension of certain real biquadratic fields

H Laxmi, Anupam Saikia

Greenberg's conjecture on the stability of $ℓ$ -class groups in the cyclotomic $Z_{ℓ}$ -extension of a real field has been proven for various infinite families of real…

math.NT2024

Unramified Iwasawa module of $Z_{2}$ -extension of certain quadratic fields with a bounded quotient

H Laxmi, Anupam Saikia

We consider an infinite family of real quadratic fields $k$ where the discriminant has three distinct odd prime factors, and the prime 2 splits. We show that the unramified Iwasawa…

math.NT2023

$Z_{2}$ -extension of real quadratic fields with $Z /2 Z$ as $2$ -class group at each layer

H Laxmi, Anupam Saikia

Let $K = Q (d)$ be a real quadratic field with $d$ having three distinct prime factors. We show that the $2$ -class group of each layer in the $Z_{2}$ -extension…

math.NT2023

On the structure and stability of ranks of $2$ -class groups in cyclotomic $Z_{2}$ -extensions of certain real quadratic fields

Jaitra Chattopadhyay, H Laxmi, Anupam Saikia

For a real quadratic field $K = Q (d)$ with discriminant $D_{K}$ having four distinct prime factors, we study the structure of the $2$ -class group $A (K_{1})$ of the f…

math.NT2022

On the $p$ -rationality of consecutive quadratic fields

Jaitra Chattopadhyay, H Laxmi, Anupam Saikia

In 2016, in the work related to Galois representations, Greenberg conjectured the existence of multi-quadratic $p$ -rational number fields of degree $2^{t}$ for any odd prime number…

Combs and complex structures on the six-sphere

Stability of 2-class groups in the Z2​-extension of certain real biquadratic fields

Unramified Iwasawa module of Z2​-extension of certain quadratic fields with a bounded quotient

Z2​-extension of real quadratic fields with Z/2Z as 2-class group at each layer

On the structure and stability of ranks of 2-class groups in cyclotomic Z2​-extensions of certain real quadratic fields

On the p-rationality of consecutive quadratic fields

Stability of 2-class groups in the $Z_{2}$ -extension of certain real biquadratic fields

Unramified Iwasawa module of $Z_{2}$ -extension of certain quadratic fields with a bounded quotient

$Z_{2}$ -extension of real quadratic fields with $Z /2 Z$ as $2$ -class group at each layer

On the structure and stability of ranks of $2$ -class groups in cyclotomic $Z_{2}$ -extensions of certain real quadratic fields

On the $p$ -rationality of consecutive quadratic fields