Asymptotic behavior of representations of graded categories with inductive functors

Gan, Wee Liang; Li, Liping

doi:10.1016/j.jpaa.2018.03.007

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Cited by 7 publications

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“…Can Theorem 1.1 be extended to positive characteristic? In positive characteristic, finiteness of regularity for finitely generated

{FI}_{d}

‐modules is [4, Theorem 1.3]. Can we bound the regularity of each

{normalR}^{i} {normalΓ}_{⩽ r} false(M false)

instead of just the complex

R {normalΓ}_{⩽ r} false(M false)

? (See Theorem 4.14 for context.…”

Section: Introductionmentioning

confidence: 99%

Regularity bounds for twisted commutative algebras

Sam

Snowden

2020

Bull. London Math. Soc.

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Let A be the twisted commutative algebra freely generated by d indeterminates of degree 1. We show that the regularity of an A-module can be bounded from the first 1 4 d 2 + 2 terms of its minimal free resolution. This partially extends results of Church and Ellenberg from the d = 1 case.Remark 1.2. Church and Ellenberg [2] proved this theorem for d = 1 in the language of FI-modules (and over any coefficient ring, with no restriction on characteristic) and gave an explicit function bounding reg(M ). Their work directly inspired this paper. Church [1] later

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“…Can Theorem 1.1 be extended to positive characteristic? In positive characteristic, finiteness of regularity for finitely generated