Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Powers of monomial ideals with characteristic-dependent Betti numbers   We explore the dependence of the Betti numbers of monomial ideals on the
characteristic of the field. A first observation is that for a fixed prime $p$
either the $i$-th Betti number of all high enough powers of a monomial ideal
differs in characteristic $0$ and in characteristic $p$ or it is the same for
all high enough powers. In our main results we provide constructions and
explicit examples of monomial ideals all of whose powers have some
characteristic-dependent Betti numbers or whose asymptotic regularity depends
on the field. We prove that, adding a monomial on new variables to a monomial
ideal, allows to spread the characteristic dependence to all powers. For any
given prime $p$, this produces an edge ideal such that the Betti numbers of all
its powers over $\mathbb{Q}$ and over $\mathbb{Z}_p$ are different. Moreover,
we show that, for every $r \geq 0$ and $i \geq 3$ there is a monomial ideal $I$
such that some coefficient in a degree $\geq r$ of the Kodiyalam polynomials
$\mathfrak P_3(I),\ldots,\mathfrak P_{i+r}(I)$ depends on the characteristic.
We also provide a summary of related results and speculate about the behaviour
of other combinatorially defined ideals.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org