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- Title
The vanishing conjecture for maps of Tor and derived splinters.
- Authors
Linquan Ma
- Abstract
We say an excellent local domain (S, n) satisfies the vanishing conditions for maps of Tor if for every A → R → S with A regular and A → R a module-finite torsion-free extension, and every A-module M, the map ToriA (M, R) → ToriA (M, S) vanishes for every i ≥ 1. Hochster-Huneke's conjecture (theorem in equal characteristic) states that regular rings satisfy such vanishing conditions [HH95]. The main theorem of this paper shows that, in equal characteristic, rings that satisfy the vanishing conditions for maps of Tor are exactly derived splinters in the sense of Bhatt [Bha12]. In particular, rational singularities in characteristic 0 satisfy the vanishing conditions. This greatly generalizes Hochster-Huneke's result [HH95] and Boutot's theorem [Bou87]. Moreover, our result leads to a new (and surprising) characterization of rational singularities in terms of splittings in module-finite extensions.
- Subjects
LOGICAL prediction; EIGENVALUES; MATHEMATICS theorems; MAPS; SPLITTING (Psychology)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2018, Vol 20, Issue 2, p315
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/768