Free $(\mathbb{Z}/p)^n$-complexes and $p$-DG modules

Jeremiah Heller; Marc Stephan

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arXiv · 1805.06854

Free $(\mathbb{Z}/p)^n$-complexes and $p$-DG modules

Jeremiah Heller·Marc Stephan

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Abstract

We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring $\mathbb{F}_p[G]$ of an elementary abelian $p$-group $G$ in terms of commutative algebra. This extends results of Carlsson for $p=2$ to all primes. As an intermediate step, we construct an embedding of the derived category of perfect chain complexes over $\mathbb{F}_p[G]$ into the derived category of $p$-DG modules over a polynomial ring.

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BibTeX RIS

Jeremiah Heller, Marc Stephan. 2018-05-17. Free $(\mathbb{Z}/p)^n$-complexes and $p$-DG modules. https://arxiv.org/abs/1805.06854

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