Monic inversion principle of local complete intersection ideal

Abstract: The renowned Quillen–Suslin Theorem is closely associated to the Affine Horrocks’ Theorem on algebraic vector bundles. It says : If $R$ is any commutative ring and $E$ is a vector bundle on $\mathbb{A}_{R}^1$ and $E$ extends to a vector bundle on $\mathbb{P}^1 _R,$ then $E$ is extended from $Spec(R).$ This is also known as "Monic inversion principle" for projective modules. Here we discuss about analogue of the Monic inversion principle for local complete intersection ideals of height $n$ in $R[T],$ where $R$ is a regular domain of dimension $d,$ which is essentially of finite type over an infinite perfect field of characteristic unequal to $2,$ and $2n \geq d + 3.$ This is a joint work with Mrinal Kanti Das and Md. Ali Zinna.

Mathematics

Audience: learners

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IIT Bombay Virtual Commutative Algebra Seminar

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