S. Mandal

activity

19962026

most citedThe Homotopy Obstructions in Complete Intersections

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

collaborators

16 papers

math.KT2026

Chow-Witt Theory in the Arrowtic Paradigm

Satya Mandal

In this article we propose a theory of Chow-Witt groups, in the paradigm of Quillen's arrow based approach to $K$ -theory. We refer to this style of arguments as arrowtic paradigm.…

math.KT2026

Nontrivial vector bundles with trivial Chern classes

Satya Mandal

Let $F_{0}$ be an algebraically closed field, with $c ha r (F_{0}) = 0$ . In this article, for prime numbers $p \geq 2$ , we construct smooth affine algebras $B$ over ${\ma…

math.AC2025

Methods in complete intersections in corank one

Satya Mandal

Let $A$ denote an affine algebra over an algebraically closed field $F$ , with $dim A = d \geq 3$ . Due to the recent exciting activities regarding projective $A$ -modules $P$ …

math.KT2024

Dévissage Hermitian Theory

Satya Mandal

We prove Dévissage theorems for Hermitian $K$ Theory (or $G W$ theory), analogous to Quillen's Dévissage theorem for $K$ -theory. For abelian categories ${\mathscr A}:=({\mathscr A},…

math.KT2023

Localization problems of Quillen

Satya Mandal

Let $X$ be a quasi projective scheme over a noetherian affine scheme $S p ec (A)$ , $U \subseteq X$ be an open subset, and $Z = X - U$ .Assume that $Z$ is complete intersection, with $k=codi…

math.AC2020★ 1 cited

Convergence of two obstructions for projective modules

Satya Mandal

Let $X = S p ec A$ denote a regular affine scheme, over a field $k$ , with $1/2 \in k$ and $dim X = d$ . Let $P$ denote a projective $A$ -module of rank $n \geq 2$ . Let $π_0\left({\mathcal…

math.AC2018★ 1 cited

Some perspective on Homotopy obstructions

Satya Mandal, Bibekananda Mishra

Throughout $A$ will denote commutative noetherian ring, with $dim A = d \geq 2$ , and $P$ denote a projective $A$ -module with $r ank (P) = n$ . In \cite{MM1} we considered the Homotopy obs…

math.AC2017

An Example in Complete Intersections and an Erratum

Satya Mandal

This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A = k [X_{1}, X_{2}, \dots, X_{n}]$ is a polynomial ring over a field $k$ . The Complete Intersection…

math.AC2016

The Monoid Structure on Homotopy Obstructions

Satya Mandal, Bibekananda Mishra

Let $A$ be a commutative noetherian ring, containing a field $k$ , with $1/2 \in k$ , $dim A = d$ , and let $P$ be a projective $A$ -module or $r ank (P) = n$ . In continuation of \cite{MM},…

math.AC2016★ 2 cited

The Homotopy Obstructions in Complete Intersections

Satya Mandal, Bibekananda Mishra

Let $A$ be a regular ring over a field $k$ , with $1/2 \in k$ and dimension $d$ . We discuss the Homotopy Conjecture of Madhav V. Nori, in the complete intersection case (meaning when…

math.AC2015

On the complete intersection conjecture of Murthy

Satya Mandal

Suppose $A = k [X_{1}, X_{2}, \dots, X_{n}]$ is a polynomial ring over a field $k$ and $I$ is an ideal in $A$ . Then M. P. Murthy conjectured that $μ (I) = μ (I / I^{2})$ , where $μ$ denotes the min…

math.AC2015

Witt, $G W$ , $K$ -theory of quasi-projective schemes

Satya Mandal

In this article we continue our investigation of the Derived Equivalences over noetherian quasi-projective schemes $X$ , over affine schemes $\spec{A}$. For integers $k \geq 0$ , let…

math.KT2014★ 1 cited

Derived Witt-Dévissage Formalism

Satya Mandal

In this article we establish some formalism of Derived Witt-Dévissage theory for resolving subcategories of abelian categories. Results directly apply to noetherian schemes.

math.KT2010

K_0 of hypersurfaces defined by x_1^2+ ... + x_n^2 = \pm 1

Manoj K Keshari, Satya Mandal

Let $k$ be a field of characteristic $\neq = 2$ and let $Q_{n, m} (x_{1}, ..., x_{n}, y_{1}, ..., y_{m}) = x_{1}^{2} + ... + x_{n}^{2} - (y_{1}^{2} + ... + y_{m}^{2})$ be a quadratic form over $k$ . Let $R(Q_{n,m})=R_{n,m…

math.AC2010

Another definition of Euler class group of a Noetherian ring

Manoj K Keshari, Satya Mandal

We will give another definition of Euler class group of a Noetherian ring.

alg-geom1996

Complete Intersections K-Theory and Chern Classes

Satya Mandal

Throughout this abstruct $A$ will denote a noetherian commutative ring of dimension $n$ . The paper has two parts. Among the interesting results in Part-1 are the following: 1) {\it…

Chow-Witt Theory in the Arrowtic Paradigm

Nontrivial vector bundles with trivial Chern classes

Methods in complete intersections in corank one

Dévissage Hermitian Theory

Localization problems of Quillen

Convergence of two obstructions for projective modules

Some perspective on Homotopy obstructions

An Example in Complete Intersections and an Erratum

The Monoid Structure on Homotopy Obstructions

The Homotopy Obstructions in Complete Intersections

On the complete intersection conjecture of Murthy

Witt, GW, K-theory of quasi-projective schemes

Derived Witt-Dévissage Formalism

K_0 of hypersurfaces defined by x_1^2+ ... + x_n^2 = \pm 1

Another definition of Euler class group of a Noetherian ring

Complete Intersections K-Theory and Chern Classes

Witt, $G W$ , $K$ -theory of quasi-projective schemes