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) …

Let A be a smooth affine domain of dimension d over an infinite perfect field k and let n be an
integer such that 2n⩾ d+ 3. Let I⊂ A [T] be an ideal of height n. Assume that I=(f1 …

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” …

Let AA be a commutative Noetherian ring and PP be a projective A A-module of rank=(dim
(A)-1)=(dim (A)-1). An intriguing open question is to find the precise obstruction for PP to split …

This article concerns a question asked by MV Nori on homotopy of sections of projective
modules defined on the polynomial algebra over a smooth affine domain R. While this …

We begin with the statement of the Riemann-Roch theorem (IF), without denominators, for
Chow groups of zero cycles. Theorem 1.1 (| F, page 297|) Suppose X is a non-singular …

Let $(R,\mathfrak {m}) $ be a regular local ring of dimension $ d $ which is essentially of
finite type over a field $ k $ such that the residue field of $ R $ is infinite. Let $ f\in\mathfrak …

Let A be a regular ring of dimension d essentially of finite type over an infinite field k of
characteristic≠ 2. Let P be a projective A-module of rank n with 2 n≥ d+ 3. Let I be an ideal …

Let A be a commutative noetherian ring, containing a field k, with 1/2∈ k, dim⁡ A= d, and let
P be a projective A-module, with rank (P)= n. Let LO (P) denote the set of all pairs (I, ω) …

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 …