English

On top dimensional Lyubeznik numbers in mixed characteristic

Commutative Algebra 2017-07-06 v2

Abstract

We prove that the top mixed characteristic Lyubeznik number of a ring SS that is a quotient of a complete unramified regular local ring of mixed characteristc with algebraically closed residue field is 11 provided that depth S2S \geq 2 and dim S3S \geq 3 using a second vanishing theorem in mixed characteristic proved in arXiv:1609.05846

Cite

@article{arxiv.1609.06372,
  title  = {On top dimensional Lyubeznik numbers in mixed characteristic},
  author = {Axel Stäbler},
  journal= {arXiv preprint arXiv:1609.06372},
  year   = {2017}
}

Comments

Unfortunately, the main result contains a mistake. One a priori only gets a surjection $E_2^{n, n-d} \to E_\infty^{n, n0d}$ for the ss in question which is too weak to conclude

R2 v1 2026-06-22T15:56:02.995Z