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6 votes

What is interesting/useful about Castelnuovo-Mumford regularity?

This question is extremely old, but I only just saw it, and I feel that I should throw in my tuppence worth. I conjectured back in a 2004 paper "Dickson invariants, regularity and computation in ...
Dave Benson's user avatar
  • 12.7k
4 votes
Accepted

Freeness of a quotient module over a regular local ring

Here is one possible way of seeing this (this is heavily inspired by an argument in Zhu's affine grassmannian notes). Choose a sequence of elements $t_1, t_2 \ldots t_n$ in $m\setminus m^2$ such that $...
afh's user avatar
  • 766
4 votes

Freeness of a quotient module over a regular local ring

Yes, because it is a maximal Cohen--Macaulay module over a regular local ring.
Sasha's user avatar
  • 37.5k
3 votes
Accepted

Proj construction and nilpotent homogenous elements in graded ring

In a commutative graded ring, the minimal prime ideals are homogeneous. See for example Lemma 10.57.8 of the Stacks Project at https://stacks.math.columbia.edu/tag/00JM. In any commutative ring, an ...
Dave Benson's user avatar
  • 12.7k
2 votes

General and translational Birkhoff lattices. Equational classes

The old question was just bumped to the top. Since it doesn't have a complete answer, I will add one. Is there an equational class between the modular class and the distributive class (different from ...
Keith Kearnes's user avatar
1 vote

Dimension of the associated graded module at an ideal

$\DeclareMathOperator{\gr}{gr}$This follows from Theorem 4.5.6 in Bruns and Herzog's Cohen-Macaulay Rings. In particular, let $R$ be a filtered ring with Noetherian filtration $F=\{I_i\}_{i\geq 0}$ (e....
mbert's user avatar
  • 133

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