Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On accumulation points of $F$-pure thresholds on regular local rings   Blickle, Musta\c{t}\u{a} and Smith proposed two conjectures on the limits of
$F$-pure thresholds. One conjecture asks whether or not the limit of a sequence
of $F$-pure thresholds of principal ideals on regular local rings of fixed
dimension can be written as an $F$-pure threshold in lower dimension. Another
conjecture predicts that any $F$-pure threshold of a formal power series can be
written as the $F$-pure threshold of a polynomial. In this paper, we prove that
the first conjecture has a counterexample but a weaker statement still holds.
We also give a partial affirmative answer to the second conjecture.

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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ex