Bounds on Bass numbers of local cohomology modules
Sayed Sadiqul Islam, Tony J. Puthenpurakal

TL;DR
This paper establishes bounds on the Bass numbers of local cohomology modules over polynomial rings, relating them to geometric properties of prime ideals and providing a systematic way to estimate their size.
Contribution
It constructs a hierarchy of prime sets and proves the existence of monotonic functions bounding Bass numbers of Lyubeznik functors, extending to compositions of local cohomology.
Findings
Existence of sets _{g}(t) covering prime ideals of fixed height.
Bounded Bass numbers by monotonic functions of geometric invariants.
Applicable to complex compositions of local cohomology functors.
Abstract
Let where is an uncountable algebraically closed field of characteristic . For a prime ideal of , let be the -th Bass number of an -module with respect to the prime . For , we construct a set such that for all and . Let be a Lyubeznik functor on . We prove that there exists some function which is monotonic in both the variables such that for all . In particular, the result holds for composition of local cohomology functors of the form $…
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics
