Positive Charakteristik/F-Signatur/Differentielle Signatur/Vergleich/Fakt/en

Let denote a local noetherian ring in positive characteristic.

If the -signature of is positive, then also the differential signature of is positive, and we have the estimate

where

If is -pure and the differential signature is positive, then also the -signature is positive. Moreover, if in this setting the differential signature exists as a limit, then the estimate

holds.