Christian Lundkvist | Searcharxiv

arXiv2008

Counterexamples regarding Symmetric Tensors and Divided Powers

We investigate the similarities and differences between the module of symmetric tensors TS^n_A(M) and the module of divided powers Γ^n_A(M). There is a canonical map Γ^n_A(M) \to TS^n_A(M) which is an isomorphism in many important cases. We give examples showing that this map need neither be surjective nor injective in general. These examples also show that the functor TS_A^n does not in general commute with base change.

math.AC↗

arXiv2007

Non-effective Deformations of Grothendieck's Hilbert Functor

Let X be a scheme that does not satisfy the valuative criterion of separatedness. We show that the Hilbert functor parametrizing closed families of X that are flat, finite and of rank one is not represented by a scheme or an algebraic space.

math.AG↗