# On the number of generators of ideals in polynomial rings

@article{Fasel2015OnTN,
title={On the number of generators of ideals in polynomial rings},
author={J. Fasel},
journal={arXiv: Commutative Algebra},
year={2015}
}
• J. Fasel
• Published 2015
• Mathematics
• arXiv: Commutative Algebra
• Let $R$ be a smooth affine algebra over an infinite perfect field $k$. Let $I\subset R$ be an ideal, $\omega_I:(R/I)^n\to I/I^2$ a surjective homomorphism and $Q_{2n}\subset \mathbb{A}^{2n+1}$ be the smooth quadric defined by the equation $\sum x_iy_i=z(1-z)$. We associate with the pair $(I,\omega_I)$ an obstruction in the set of homomorphisms $\mathrm{Hom}_{\mathbb{A}^1}(\mathrm{Spec}(R),Q_{2n})$ up to naive homotopy whose vanishing is sufficient for $\omega_I$ to lift to a surjection \$R^n\to… CONTINUE READING
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