V. Sadhu

activity

20142024

most citedRelative Cartier divisors and K-theory

2 citations · 2 across the 7 of their papers we have counts for

collaborators

11 papers

math.AG2024

On the vanishing of Twisted negative K-theory and homotopy invariance

Vivek Sadhu

In this article, we revisit Weibel's conjecture for twisted $K$ -theory. We also examine the vanishing of twisted negative $K$ -groups for Prüfer domains. Furthermore, we observe tha…

math.KT2023

Lambda Module structure on higher $K$ -groups

Sourayan Banerjee, Vivek Sadhu

In this article, we show that for a quasicompact scheme $X$ and $n > 0,$ the $n$ -th $K$ -group $K_{n} (X)$ is a $λ$ -module over a $λ$ -ring $K_{0} (X)$ in the sense of Hesselholt.

math.KT2023

On the generators of Nil $K$ -groups

Sourayan Banerjee, Vivek Sadhu

In this article, we study higher Nil $K$ -groups via binary complexes. More particularly, we exhibit an explicit form of generators of higher Nil $K$ -groups in terms of binary compl…

math.AG2021

The Brauer group of a valuation ring

Vivek Sadhu

Let $V$ be a valuation ring and $K$ be its field of fraction. We show that the canonical map $\Br(V) \to \Br(K)$ is injective.

math.AG2020

Equivariant Picard groups and Laurent polynomials

Vivek Sadhu

Let $G$ be a finite group. For a $G$ -ring $A,$ let $Pic^{G} (A)$ denote the equivariant Picard group of $A .$ We show that if $A$ is a finite type algebra over a fiel…

math.AG2020

Projective bundle formula for Heller' relative K_0

Vivek Sadhu

In this article, we study the Heller relative $K_{0}$ group of the map $P_{X}^{r} \to P_{S}^{r},$ where $X$ and $S$ are quasi-projective schemes over a commutativ…

math.AG2019

Relative Brauer Groups and étale cohomology

Vivek Sadhu

In this article, we construct a natural group homomorphism $ψ : Br (f) \to H_{e t}^{1} (S, f_{*} O_{X}^{\times} / O_{S}^{\times})$ for a faithful affine map $…

math.AG2017

On the vanishing of Relative Negative K-theory

Vivek Sadhu

In this article, we study the relative negative K-groups $K_{- n} (f)$ of a map $f : X \to S$ of schemes. We prove a relative version of the Weibel conjecture i.e. if $f : X \to S$ is…

math.KT2016★ 2 cited

Relative Cartier divisors and K-theory

Vivek Sadhu, Charles Weibel

We study the relative Picard group $P i c (f)$ of a map $f : X \to S$ of schemes. If $f$ is faithful affine, it is the relative Cartier divisor group $I (f)$ . The relative group $K_{0} (f)$ …

math.AC2015

Relative Cartier Divisors and Laurent Polynomial Extensions

Vivek Sadhu, Charles Weibel

If $i : A \subset B$ is a commutative ring extension, we show that the group $I (A, B)$ of invertible $A$ -submodules of $B$ is contracted in the sense of Bass, with $L\mathcal…

math.AC2014

Subintegrality, Invertible Modules and Laurent Polynomial Extensions

Vivek Sadhu

Let $A \subseteq B$ be a commutative ring extension. Let $I (A, B)$ be the multiplicative group of invertible $A$ -submodules of $B$ . In this article, we extend a result of S…

On the vanishing of Twisted negative K-theory and homotopy invariance

Lambda Module structure on higher K-groups

On the generators of Nil K-groups

The Brauer group of a valuation ring

Equivariant Picard groups and Laurent polynomials

Projective bundle formula for Heller' relative K_0

Relative Brauer Groups and étale cohomology

On the vanishing of Relative Negative K-theory

Relative Cartier divisors and K-theory

Relative Cartier Divisors and Laurent Polynomial Extensions

Subintegrality, Invertible Modules and Laurent Polynomial Extensions

Lambda Module structure on higher $K$ -groups

On the generators of Nil $K$ -groups