Tariq Syed

activity

20172026

most citedThe cancellation of projective modules of rank 2 with a trivial determinant

5 citations · 10 across the 13 of their papers we have counts for

collaborators

13 papers

math.AG2026

Vector bundles over certain Koras-Russell threefolds of the third kind

Tariq Syed

Let $k$ be an algebraically closed base field of characteristic $0$ and let $α_{1}, α_{2}, α_{3}, d \geq 2$ be integers such that $α_{1}, α_{2}, α_{3}$ are pairwise coprime and $gc…

math.AG2025

Efficient generation of projective modules: a motivic view

Aravind Asok, Morgan Opie, Brian Shin +1

Assume $k$ is a field and $R$ is a smooth $k$ -algebra of dimension $d$ . If $P$ is a projective module of rank $r$ , then it is well-known that $P$ can be generated by $r + d$ -elements…

math.AC2025

Stably free modules of rank $2$ over certain real smooth affine threefolds

Tariq Syed

Let $R$ be a real smooth affine domain of dimension $3$ such that $R$ has either no real maximal ideals or the intersection of all real maximal ideals in $R$ has height at least $1…

math.AG2025

On algebraic vector bundles of rank $2$ over smooth affine fourfolds

Thomas Brazelton, Morgan Opie, Tariq Syed

The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquel…

math.AG2024

The generalized Vaserstein symbol revisited

Tariq Syed

We give a construction of a generalized Vaserstein symbol associated to any finitely generated projective module of rank $2$ over a commutative ring with unit.

math.AG2024

A symplectic version of Suslin's $n!$ -theorem

Tariq Syed

We prove symplectic versions of Suslin's famous $n!$ -theorem for algebras over quadratically closed perfect fields of characteristic $\neq = 2$ and for algebras over finite fields of…

math.AC2024

A note on Suslin matrices and Clifford algebras

Tariq Syed

We give a conceptual explanation for the somewhat mysterious origin of Suslin matrices. This enables us to generalize the construction of Suslin matrices and to give more conceptua…

math.AG2023

Some remarks on Spin-orbits of unit vectors

Tariq Syed

For $n \in N$ and a commutative ring $R$ with $2 \in R^{\times}$ , the group $S L_{n} (R)$ acts on the set $U m_{n} (R)$ of unimodular vectors of length $n$ and $S p i n_{2 n} (R)$ ac…

math.AG2023

Motivic cohomology of cyclic coverings

Tariq Syed

Cyclic coverings produce many examples of topologically contractible smooth affine complex varieties. In this paper, we study the motivic cohomology groups of cyclic coverings over…

math.AG2020

Cancellation of vector bundles of rank $3$ with trivial Chern classes on smooth affine fourfolds

Tariq Syed

If $n \equiv 0, 1 m o d 4$ , we prove a sum formula $V_{θ_{0}} (a_{0}, a_{R}^{n}) = n \cdot V_{θ_{0}} (a_{0}, a_{R})$ for the generalized Vaserstein symbol whenever $R$ is a smooth affin…

math.AG2020

Symplectic orbits of unimodular rows

Tariq Syed

For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and an invertible alternating matrix $χ$ of rank $2 n$ , the group $S p (χ)$ of invertible matrices of rank $2n…

math.AG2019★ 5 cited

The cancellation of projective modules of rank 2 with a trivial determinant

Tariq Syed

We study the cancellation property of projective modules of rank $2$ with a trivial determinant over Noetherian rings of dimension $\leq 4$ . If $R$ is a smooth affine algebra of di…

math.AG2017★ 5 cited

A generalized Vaserstein symbol

Tariq Syed

Let $R$ be a commutative ring. For any projective $R$ -module $P_{0}$ of constant rank $2$ with a trivialization of its determinant, we define a generalized Vaserstein symbol on the o…

Vector bundles over certain Koras-Russell threefolds of the third kind

Efficient generation of projective modules: a motivic view

Stably free modules of rank 2 over certain real smooth affine threefolds

On algebraic vector bundles of rank 2 over smooth affine fourfolds

The generalized Vaserstein symbol revisited

A symplectic version of Suslin's n!-theorem

A note on Suslin matrices and Clifford algebras

Some remarks on Spin-orbits of unit vectors

Motivic cohomology of cyclic coverings

Cancellation of vector bundles of rank 3 with trivial Chern classes on smooth affine fourfolds

Symplectic orbits of unimodular rows

The cancellation of projective modules of rank 2 with a trivial determinant

A generalized Vaserstein symbol

Stably free modules of rank $2$ over certain real smooth affine threefolds

On algebraic vector bundles of rank $2$ over smooth affine fourfolds

A symplectic version of Suslin's $n!$ -theorem

Cancellation of vector bundles of rank $3$ with trivial Chern classes on smooth affine fourfolds