IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

For a Cohen-Macaulay ring R, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite projective dimension modules with the bounded derived category of projective modules with finite length homologies. This yields isomor-phisms of K-theory and Witt groups (amongst other invariants) and improves on terms of associated spectral sequences and Gersten complexes. © 2016 American Mathematical Society.

Department of Mathematics

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Transactions of the American Mathematical Society

Finite homological dimension and a derived equivalence

In this paper we extend and apply the work of Paul Balmer and others on derived and triangular Witt Groups. We obtain a generalized form of dévissage for derived Witt Groups over Cohen-Macaulay rings. 2000 Mathematics Subject Classification: Primary: 11E81, 18E30, 19G12; Secondary: 13C10, 13D. © 2016, Ramanujan Mathematical Society. All rights reserved.

Journal of the Ramanujan Mathematical Society

On Dévissage for Witt groups

We consider bounded complexes P<inf>•</inf> of finitely generated projective A-modules whose homologies have finite projective dimension and are locally Cohen-Macaulay. We give a necessary and sufficient condition so that its dual P•* also has the same property. © 2015.

Journal of Algebra

Stability of locally CMFPD homologies under duality

We exhibit an example of a smooth affine threefold over a field of characteristic for which there exist non-trivial 2-torsion elements in the Euler class group vanishing in the weak Euler class group . This gives a positive answer to a question of the first author and Raja Sridharan.

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Journal of Pure and Applied Algebra

Euler class groups and 2-torsion elements

Let X = Spec (A) be a smooth, affine variety of dimension n ≥ 2 over the field R of real numbers. Let P be a projective A-module of rankn such that its nth Chern class Cn (P) ∈ CH0 (X) is zero. In this set-up, Bhatwadekar-Das-Mandal showed (amongst many other results) that P ≃ A ⊕ Q in the case that either n is odd or the topological space X (R) of real points of X does not have a compact, connected component. In this paper, we prove that similar results hold for smooth, affine varieties over an arbitrary real closed field R. The proof is algebraic and does not make use of Tarski's principle, nor of the earlier result for R. © 2009 Elsevier Inc. All rights reserved.

Projective modules over smooth, affine varieties over real closed fields

Let X = Spec (A) be a smooth, affine variety of dimension n ≥ 2 over the field R of real numbers. Let P be a projective A-module of rank n such that its nth Chern class Cn (P) ∈ CH0 (X) is zero. In this set-up, Bhatwadekar-Das-Mandal showed (amongst many other results) that P ≃ A ⊕ Q in the case that either n is odd or the topological space X (R) of real points of X does not have a compact, connected component. In this paper, we prove that similar results hold for smooth, affine varieties over an Archimedean real closed field R. © 2009 Elsevier B.V. All rights reserved.