Corpus ID: 119559593

# FI-modules and the cohomology of modular representations of symmetric groups

@article{Nagpal2015FImodulesAT,
title={FI-modules and the cohomology of modular representations of symmetric groups},
author={Rohit Nagpal},
journal={arXiv: Representation Theory},
year={2015}
}
• Rohit Nagpal
• Published 2015
• Mathematics
• arXiv: Representation Theory
• An FI-module $V$ over a commutative ring $\bf{k}$ encodes a sequence $(V_n)_{n \geq 0}$ of representations of the symmetric groups $(\mathfrak{S}_n)_{n \geq 0}$ over $\bf{k}$. In this paper, we show that for a "finitely generated" FI-module $V$ over a field of characteristic $p$, the cohomology groups $H^t(\mathfrak{S}_n, V_n)$ are eventually periodic in $n$. We describe a recursive way to calculate the period and the periodicity range and show that the period is always a power of $p$. As an… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 38 REFERENCES

## Representation stability and finite linear groups

• Mathematics
• 2017
VIEW 1 EXCERPT

## Gröbner methods for representations of combinatorial categories

• Mathematics
• 2016

## Improved homological stability for configuration spaces after inverting $2$

• Mathematics
• 2015

## On Homological Stability for Configuration Spaces on Closed Background Manifolds

• Mathematics
• 2015

## Cohomologie des foncteurs polynomiaux sur les groupes libres

• Mathematics
• 2014
VIEW 1 EXCERPT

## Homological stability for automorphism groups

• Mathematics
• 2014
VIEW 1 EXCERPT

• N. Wahl
• 2014

## Uniformly presented vector spaces, arXiv:1406.0786v1

• J. Wiltshire-Gordon
• 2014