Homology of FI-modules

By Thomas Church, Jordan S. Ellenberg. 2015

95 citations recorded by the source corpus.

We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V in terms of the degrees of its generators and relations. We use this to refine a result of Putman on the stability of homology of congruence subgroups, extending his theorem to previously excluded small characteristics and to integral homology while maintaining explicit bounds for the stable range.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/23f107a2852b11b576a1d66a790fda2ba9b3d76b

How researchers see this paper

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In Algebra and Number Theory

1. O. Randal-Williams
2. Uwe Nagel
3. Nathalie Wahl
4. Tim Romer
5. Juan Migliore
6. Karim A. Adiprasito

In Computational Theory and Mathematics

1. Nathalie Wahl
2. O. Randal-Williams
3. Uwe Nagel
4. Tim Romer
5. Juan Migliore
6. Karim A. Adiprasito

In Mathematical Physics

1. O. Randal-Williams
2. Nathalie Wahl
3. Uwe Nagel
4. Tim Romer
5. Michael Weiss
6. Søren Galatius
7. Pedro Boavida de Brito
8. Andrew Putman

Citations in the corpus

• Higher-order representation stability and ordered configuration spaces of manifolds (2016, unknown): “We begin by recalling the definition of configuration spaces and their stabilization maps in Section 3.1.”
• FI- and OI-modules with varying coefficients (2017, background): “Results of this kind appeared in [2, 20, 21, 23, 25]; see the discussion in Remark 7.”
• Homological stability for automorphism groups (2014, background): “8 in [17] and its proof: Equation (18) in the proof holds for p = 0 and a = j + 1 ≥ 1, and by the theorem, the middle term is “of degree” d+min(r, d)−1− (j+1) = d+min(r, d)−j−2,”