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# Mathematical Research Letters

## Volume 17 (2010)

### Number 2

### Free resolutions over commutative Koszul algebras

Pages: 197 – 210

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n2.a1

#### Authors

#### Abstract

For $R=Q/J$ with $Q$ a commutative $\BN$-graded algebra over a field and $J\ne0$, we relate the slopes of the minimal resolutions of $R$ over $Q$ and of $k=R/R_{+}$ over $R$. When $Q$ and $R$ are Koszul and $J_1=0$ we prove $\Tor iQ{R}k_j=0$ for $j >2i\ge0$, and also for $j=2i$ when $i >\dim Q-\dim R$ and $\pd_QR$ is finite.