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

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.

### 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
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