“Serre's Conjecture”, for the most part of the second half of the 20th century,-ferred to the
famous statement made by J.-P. Serre in 1955, to the effect that one did not know if? nitely …

We give an arithmetic count of the lines on a smooth cubic surface over an arbitrary
field,\[\sum_ {\text {lines}}\operatorname {Tr} _ {L/k}\langle\alpha\rangle= 15\cdot\langle …

For a commutative Noetherian ring A of finite Krull dimension containing the field of rational
numbers, an Abelian group called the Euler class group is defined. An element of this group …

We enrich the classical count that there are two complex lines meeting four lines in space to
an equality of isomorphism classes of bilinear forms. For any field $ k $, this enrichment …

Let A be a smooth affine domain of dimension n over a field k and I be a prime ideal of A [T]
of height r such that A [T]/I is smooth and 2r≥ n+ 3. Let f1 (T),···, fr (T)∈ I such that I=(f1 (T) …

The famous Quillen's Local Global (LG) Principle determines that a finitely presented
module over a polynomial ring R [X] over a commutative ring R is extended if it is “locally” …

In [13, Section 5], Murthy defined the “Segre class” of a finitely generated module M over a
smooth affine domain A over an algebraically closed field k. The Segre class of M, denoted …

The aim of this expository paper is to give a self contained account which is accessible to
students of some of the work done by Indian mathematicians in the field of projective …

In this paper we prove the moving lemma, the addition and subtraction principles, in a more
general setup than the available ones. We apply these results to explore a question of Nori …

Let A be a Noetherian ring of dimension n and P be a projective A module of rank n having
trivial determinant. It is proved that if n is even and the image of a generic element g∈ P* is …