Efficient generation of ideals in a discrete Hodge algebra

TL;DR

This paper proves the triviality of certain Euler class groups in discrete Hodge algebras over Noetherian rings, providing new insights into algebraic ideal generation in these structures.

Contribution

It establishes the triviality of top and near-top Euler class groups in discrete Hodge algebras, advancing understanding of ideal generation in algebraic geometry.

Findings

Top Euler class group $E^d(D)$ is trivial.

If $d > ext{dim}(R)+1$, then $E^{d-1}(D)$ is trivial.

Results apply to algebraic structures over Noetherian rings.

Abstract

Let $R$ be a commutative Noetherian ring and $D$ be a discrete Hodge algebra over $R$ of dimension $d>\text{dim}(R)$. Then we show that (i) the top Euler class group $E^d(D)$ of $D$ is trivial. (ii) if $d>\text{dim}(R)+1$, then $(d-1)$-st Euler class group $E^{d-1}(D)$ of $D$ is trivial.