Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals
نویسندگان
چکیده
منابع مشابه
Frobenius actions on the de Rham cohomology of Drinfeld modules
We study the action of endomorphisms of a Drinfeld A-module φ on its de Rham cohomology HDR(φ,L) and related modules, in the case where φ is defined over a field L of finite Acharacteristic p. Among others, we find that the nilspace H0 of the total Frobenius FrDR on HDR(φ,L) has dimension h = height of φ. We define and study a pairing between the p-torsion pφ of φ and HDR(φ,L), which becomes pe...
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A modification of Katzman’s example is given to produce a two-generated ideal in a two-dimensional Noetherian integral domain for which the set of associated primes of all the Frobenius powers is infinite. A further modification yields a four-dimensional Noetherian integral domain and a five-dimensional Noetherian local integral domain for which an explicit second local cohomology module has in...
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We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include unique factorization domains of characteristic zero with rational singularities, as well as F-regular unique factorization domains of positive characteristic. As a consequence, we answer a question on the associated primes of Frobenius powers of ideals, which arose from the loc...
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A modiication of Katzman's example is given to produce a two-generated ideal in a two-dimensional Noetherian integral domain for which the set of associated primes of all the Frobenius powers is innnite. A further modiication yields a four-dimensional Noetherian integral domain and a ve-dimensional Noetherian local integral domain for which an explicit second local cohomology module has innnite...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2019
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.03.015