On the (non)rigidity of the Frobenius endomorphism over Gorenstein rings. (English) Zbl 1221.13004

Dao, Hailong; Li, Jinjia; Miller, Claudia

Algebra Number Theory 4, No. 8, 1039-1053 (2010).

An immediate corollary of the main result of the paper presents torsion-freeness of punctured spectrum of an equicharacteristic local complete intersection ring of dimension 3, by using homological properties of the Frobenius map, e.g. Tor-rigidity of the Frobenius map. This is a local version of a result of Deligne.

Reviewer: Mohsen Asgharzadeh (Tehran)

MSC:

13A35	Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure
13D07	Homological functors on modules of commutative rings (Tor, Ext, etc.)
13H10	Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)

Keywords:

Frobenius endomorphism; rigidity; tor; Picard group