linear map to dual space

Stream: maths

[Scott Carnahan]

Is there a good name for a distinguished map from a vector space (or module) to its dual? For abelian varieties, we say polarization for an isogeny to the dual, but I think I have seen that word used for other, possibly similar notions in functional analysis. The reason I am asking is that in SGA3 Exp XXI section 1.2 Demazure introduces such a map from weight space to its dual, and calls it p, which is not really an acceptable name for mathlib.

[Johan Commelin]

For a Hodge structure it would also be called "polarization". I guess it depends on who you ask whether a Hodge structure is more like an abelian variety or more like a vector space...

[Johan Commelin]

@Jireh Loreaux @Sébastien Gouëzel eager to hear whether you think "polarization" would be ambiguous.

[Matthew Ballard]

:+1: for polarization but I suffer from the same training here I fear

[Johan Commelin]

Mildly relevant: docs#Module.DualBases

[Oliver Nash]

Distinguished bilinear form?