Mast Kalandar

bandar's colander of random jamun aur aam

Sat, 07 Feb 2015

Serre's Problem and Indian Mathematicians

india, math, mathematics, projective modules [link] [comments ()] [raw]

Of late, I have been trying to fill up a gap in my education and learn how it is proved that vector bundles on affine n-space are trivial. More generally, it has been shown that if X is a smooth affine variety then a vector bundle on X × L, where L is an affine line, is pulled back from X.

A standard resource for this material is T. Y. Lam's book on ``Serre's Problem on Projective Modules''. While reading this book, I realised that this is a topic on which Indian Mathematicians, mostly working within India, have made many significant contributions. (The fact that Serre's problem was actually settled by Quillen and Suslin, who are not Indian is only marginally important!) In particular, one can note that no less than 30 Mathematicians of this kind are referred to in Lam's book.

I was at the School of Mathematics, TIFR during the period when mathematicians there were in the thick of this activity. In hindsight, it is clear that I missed a golden opportunity to learn about it and appreciate it then! Still, better late than never ...

In this context, it is odd that some people think that we need to go back thousands of years to find significant contributions to Mathematics from India. All of the work mentioned above started only about 50 years ago and continues till today. Moreover, the problem (which is related to that of solving linear equations) is centuries old.

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