Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Test ideals via a single alteration and discreteness and rationality of
  $F$-jumping numbers   Suppose $(X, \Delta)$ is a log-$\bQ$-Gorenstein pair. Recent work of M.
Blickle and the first two authors gives a uniform description of the multiplier
ideal $\mJ(X;\Delta)$ (in characteristic zero) and the test ideal
$\tau(X;\Delta)$ (in characteristic $p > 0$) via regular alterations. While in
general the alteration required depends heavily on $\Delta$, for a fixed
Cartier divisor $D$ on $X$ it is straightforward to find a single alteration
(e.g. a log resolution) computing $\mJ(X; \Delta + \lambda D)$ for all $\lambda
\geq 0$. In this paper, we show the analogous statement in positive
characteristic: there exists a single regular alteration computing $\tau(X;
\Delta + \lambda D)$ for all $\lambda \geq 0$. Along the way, we also prove the
discreteness and rationality for the $F$-jumping numbers of $\tau(X; \Delta+
\lambda D)$ for $\lambda \geq 0$ where the index of $K_X + \Delta$ is arbitrary
(and may be divisible by the characteristic).

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The categories of this paper are: cs
7
The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin