Manuscript XV-B@2 · XV-B.tex · definition · 4d3f12e8

Definition: Relation filtration for natural lifts

Natural null defects and point-puncture corrections › Finite-jet localization of the defect · lines 1349–1372

XV-B@2#def:relationfiltration

In the preceding smooth-locus setting, put

H_{univ} = {a : f_{γ} (a) = 0 on X for every γ},

and

H_{flat} = {a \in H^{\circ} : f_{γ} (a) is flat along Z for every γ} .

Then

H_{univ} \subset H_{flat} \subset H^{\circ} .

The successive categories are called universal relations, non-universal flat-annihilator relations, and potentially jet-detected relations.

Displayed formulas in this passage

unlabeled · line 1352
$H_{univ} = {a : f_{γ} (a) = 0 on X for every γ},$
unlabeled · line 1357
$H_{flat} = {a \in H^{\circ} : f_{γ} (a) is flat along Z for every γ} .$
unlabeled · line 1364
$H_{univ} \subset H_{flat} \subset H^{\circ} .$