Sampat Sharma

activity

20172022

most citedNice group structure on the elementary orbit space of unimodular rows

3 citations · 4 across the 8 of their papers we have counts for

collaborators

11 papers

math.KT2022

Generalised homotopy and commutativity principle

Ravi A. Rao, Sampat Sharma

In this paper, we study the action of special $n \times n$ linear (resp. symplectic) matrices which are homotopic to identity on the right invertible $n \times m$ matrices. We also…

math.RA2022

Unimodular rows over affine algebras over algebraic closure of a finite field

Sampat Sharma

In this article, we prove that if $R$ is an affine algebra of dimension $d \geq 4$ over $F_{p}$ and $1/ (d - 1)! \in R,$ then any unimodular row over $R$ of length…

math.KT2021

Applications of Swan's Bertini to unimodular rows

Manoj K. Keshari, Sampat Sharma

Let $R$ be an affine algebra of dimension $d \geq 4$ over a perfect field $k$ of char $\neq = 2$ and $I$ be an ideal of $R$ . Then - Um $_{d + 1} (R, I) / E_{d + 1} (R, I)$ has nice group s…

math.AC2021

Generalised Mennicke-Newman lemma

Sampat Sharma

Mennicke--Newman lemma for unimodular rows was used by W. van der Kallen to give a group structure on the orbit set $\frac{U m _{n} ( R )}{E _{n} ( R )}$ for a commutative noetherian ring o…

math.AC2021★ 3 cited

Nice group structure on the elementary orbit space of unimodular rows

Manoj K. Keshari, Sampat Sharma

(1) If $R$ is an affine algebra of dimension $d \geq 4$ over $F_{p}$ with $p > 3$ , then the group structure on $Um_{d} (R) / E_{d} (R)$ is nice. (2) If $R$ is…

math.AC2021

Completion of skew completable unimodular rows

Sampat Sharma

Skew completable unimodular rows of odd length are completable over polynomial extension of a local ring if dimension of local ring and length of unimodular rows are same.

math.AC2020

Absence of torsion in orbit space

Sampat Sharma

In this paper, we prove that if $R$ is a local ring of dimension $d,$ $d \geq 2$ and $\frac{1}{d !} \in R$ then the group $\frac{U m _{d + 1} ( R [ X ])}{E _{d + 1} ( R [ X ])}$ has no $k$ -torsion, pr…

math.AC2020

On completion of unimodular rows over polynomial extension of finitely generated rings over $Z$

Sampat Sharma

In this article, we prove that if $R$ is a finitely generated ring over $Z$ of dimension $d, d \geq 2, \frac{1}{d !} \in R$ , then any unimodular row over $R [X]$ of length $d+1…

math.AC2020★ 1 cited

The quotient Unimodular Vector group is nilpotent

Reema Khanna, Selby Jose, Sampat Sharma +1

Jose-Rao introduced and studied the Special Unimodular Vector group $S U m_{r} (R)$ and $E U m_{r} (R)$ , its Elementary Unimodular Vector subgroup. They proved that for $r \geq 2$ , $EUm_r(R)…

math.AC2020

On the first row map $G L_{d + 1} (R) ⟶ \frac{U m _{d + 1} ( R )}{E _{d + 1} ( R )}$

Sampat Sharma

In this paper, we prove that there is group homomorphism from general linear group over a polynomial extension of a local ring to the W. van der Kallen group.

math.AC2017

Homotopy and Commutativity Principle

Ravi A. Rao, Sampat Sharma

In this article, we prove commutativity principal for linear, symplectic and transvection groups. This principle is a consequence of Quillen-Suslin local global principle and using…

Generalised homotopy and commutativity principle

Unimodular rows over affine algebras over algebraic closure of a finite field

Applications of Swan's Bertini to unimodular rows

Generalised Mennicke-Newman lemma

Nice group structure on the elementary orbit space of unimodular rows

Completion of skew completable unimodular rows

Absence of torsion in orbit space

On completion of unimodular rows over polynomial extension of finitely generated rings over Z

The quotient Unimodular Vector group is nilpotent

On the first row map GLd+1​(R)⟶Ed+1​(R)Umd+1​(R)​

Homotopy and Commutativity Principle

On completion of unimodular rows over polynomial extension of finitely generated rings over $Z$

On the first row map $G L_{d + 1} (R) ⟶ \frac{U m _{d + 1} ( R )}{E _{d + 1} ( R )}$