Length of local cohomology of powers of ideals

Hailong Dao; Jonathan Montaño

doi:10.1090/tran/7402

Length of local cohomology of powers of ideals

Transactions of the American Mathematical Society ◽

10.1090/tran/7402 ◽

2018 ◽

Vol 371 (5) ◽

pp. 3483-3503 ◽

Cited By ~ 1

Author(s):

Hailong Dao ◽

Jonathan Montaño

Keyword(s):

Local Cohomology ◽

Powers Of Ideals

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On local cohomology and Hilbert function of powers of ideals

manuscripta mathematica ◽

10.1007/s00229-003-0393-1 ◽

2003 ◽

Vol 112 (1) ◽

pp. 77-92 ◽

Cited By ~ 2

Author(s):

L� Tu�n Hoa ◽

Eero Hyry

Keyword(s):

Hilbert Function ◽

Local Cohomology ◽

Powers Of Ideals

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Limit behavior of the rational powers of monomial ideals

Journal of Algebra and Its Applications ◽

10.1142/s021949882350069x ◽

2021 ◽

Author(s):

James Lewis

Keyword(s):

Local Cohomology ◽

Integral Closure ◽

Monomial Ideals ◽

Limit Behavior ◽

Associated Primes ◽

Powers Of Ideals ◽

Symbolic Powers ◽

Local Cohomology Modules ◽

Cohomology Modules

We investigate the rational powers of ideals. We find that in the case of monomial ideals, the canonical indexing leads to a characterization of the rational powers yielding that symbolic powers of squarefree monomial ideals are indeed rational powers themselves. Using the connection with symbolic powers techniques, we use splittings to show the convergence of depths and normalized Castelnuovo–Mumford regularities. We show the convergence of Stanley depths for rational powers, and as a consequence of this, we show the before-now unknown convergence of Stanley depths of integral closure powers. Additionally, we show the finiteness of asymptotic associated primes, and we find that the normalized lengths of local cohomology modules converge for rational powers, and hence for symbolic powers of squarefree monomial ideals.

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