In the 70s Breen discovered that if one computes Ext groups between two commutative group schemes (considered as flat sheaves of abelian groups) then typically there are some “parasitic” non-zero classes in high degrees which do not really carry any algebro-geometric meaning. This has some unpleasant consequences for deformation theory: for example, the cotangent complex in the corresponding derived moduli spaces turns out to be unbounded. I will talk about joint project with A.Mathew, A.Raksit and B.Zavyalov where we study the so-called “sheaves with multiplicative polynomial transfers”. We propose the corresponding category as a more suitable home for doing homological algebra with commutative group schemes (as opposed to general sheaves). In particular, we show that Ext-groups at least between some group schemes behave much better in this setting. Consequently, this allows for a better behaved notion of a “derived commutative group scheme“. If time permits, I will also discuss how our computations allow to revisit and generalize the original computations of Breen.