arXiv subjects

Subham Sarkar

Publications and source records attributed to Subham Sarkar.

7 recordsLinked to original sources

arXiv2025

GEMMA-SQL: A Novel Text-to-SQL Model Based on Large Language Models

Text-to-SQL systems enable users to interact with structured databases using natural language, eliminating the need for specialized programming knowledge. In this work, we introduce GEMMA-SQL, a lightweight and efficient text-to-SQL model built upon the open-source Gemma 2B architecture. Unlike many large language models (LLMs), GEMMA-SQL is fine-tuned in a resource-efficient, iterative manner and can be deployed on low-cost hardware. Leveraging the SPIDER benchmark for training and evaluation, GEMMA-SQL combines multiple prompting strategies, including few-shot learning, to enhance SQL query generation accuracy. The instruction-tuned variant, GEMMA-SQL Instruct, achieves 66.8% Test-Suite accuracy and 63.3% Exact Set Match accuracy, outperforming several state-of-the-art baselines such as IRNet, RYANSQL, and CodeXDavinci. The proposed approach demonstrates that effective prompt design and targeted instruction tuning can significantly boost performance while maintaining high scalability and adaptability. These results position GEMMA-SQL as a practical, open-source alternative for robust and accessible text-to-SQL systems.

cs.CL↗

arXiv2022

On Perverse sheaves of a Coxeter hyperplane arrangement of type $\mathcal{A}_n$

Kapranov and schechtman gave quiver description of perverse sheaves on real hyperplane arrangements. We used this description to relate the perverse sheaves on Coxeter hyperplane arrangements of type $\mathcal A_n$ for different values of $n$. As a consequence we prove that the simple perverse sheaves whose stalk on open cells are zero are induced from the perverse sheaves on lower dimension arrangements.

math.AG↗

arXiv2022

The fundamental group and extensions of motives of Jacobians of curves

In this paper we construct extensions of mixed Hodge structures coming from the mixed Hodge structure on the graded quotients of the group ring of the fundamental group of a smooth, projective, pointed curve. These extensions correspond to the regulators of certain motivic cycles in the Jacobian of the curve which were constructed by Beilinson and Bloch. This leads to a new iterated integral expression for the regulator. This is a generalisation of a theorem of Colombo where she constructed the extension corresponding to Collino's cycles in the Jacobian of a hyperelliptic curve.

math.AG↗

arXiv2022

A Base Change Version of Rasmussen-Tamagawa Conjecture

We prove a certain uniform version of the Shafarevich Conjecture. As a corollary, we prove the Rasmussen-Tamagawa Conjecture for a particular class of abelian varieties $A$ defined over a number $K$ of dimension $g$ having everywhere potential good reduction, in particular, for any finite place $v$ of $K$ the localization $A_v:=A\times_{\mathrm{Spec}(K)}\mathrm{Spec}(K_v)$ has either good reduction or {\it totally bad reduction} (connected component $\tilde{\mathcal{A}}_v^0$ of the special fibre $\tilde{\mathcal{A}}_v$ of the N\'eron model $\mathcal{A}_v$ at $v$ is an affine group scheme over the residue field $k_v$ at $v$) and has good reduction over a quadratic extension of $K_v$.

math.NT↗

arXiv2021

An Equisingular Specialisation of the Compactified Jacobian and its applications

For any positive integer $k$, let $X_k$ be a projective irreducible nodal curve with $k$ nodes. We show that the Betti numbers and the mixed Hodge numbers of the compactified Jacobian $\overline{J_{k}}$ of an irreducible nodal curve $X_k$ with $k$ nodes are the same as the Betti numbers and the mixed Hodge numbers of $J_0\times R^k$, where $J_0$ is the Jacobian of the normalisation of the irreducible nodal curve and $R$ denotes the rational nodal curve with one node. We prove it by constructing a topologically locally trivial family of projective varieties containing $\overline{J_{k}}$ and $J_0\times R^k$ as fibres.

math.AG↗

arXiv2017

Higher Chow cycles on Jacobian of Fermat curves and Hypergeometric functions

In this paper we construct certain higher Chow cycles in the $K_{1}$ of the Jacobian of Fermat curves, generalising a construction of Collino. We further compute the regulator of these elements in terms of special values of hypergeometric functions. Otsubo has computed the regulator of certain elements of $K_0$ and $K_2$ of Fermat varieties and this paper is along the same lines.

math.NT↗

arXiv2014

Extensions of Motives and the Fundamental Group

In this paper we construct extensions of the Mixed Hodge structure on the fundamental group of a pointed algebraic curve. These extensions correspond to the regulator of certain explicit motivic cohomology cycles in the self product of the curve which were first constructed by Bloch and Beilinson. This leads to a new iterated integral expression for the regulator. Our result is a generalization of a result of Colombo's where she constructs the extension corresponding to a motivic cycle class in the Jacobian of a hyperelliptic curve constructed by Collino. This is to appear in the Mathematical Proceedings of the Indian Academy of Sciences.

math.AG↗