Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constant families of t-structures on derived categories of coherent
  sheaves   We generalize the construction given in math.AG/0309435 of a "constant"
t-structure on the bounded derived category of coherent sheaves $D(X\times S)$
starting with a t-structure on $D(X)$. Namely, we remove smoothness and
quasiprojectivity assumptions on $X$ and $S$ and work with t-structures that
are not necessarily Noetherian but are close to Noetherian in the appropriate
sense. The main new tool is the construction of induced t-structures that uses
unbounded derived categories of quasicoherent sheaves and relies on the results
of \cite{AJS}. As an application of the "constant" t-structures techniques we
prove that every bounded nondegenerate t-structure on $D(X)$ with Noetherian
heart is invariant under the action of a connected group of autoequivalences of
$D(X)$. Also, we show that if $X$ is smooth then the only local t-structures on
$D(X)$, i.e., those for which there exist compatible t-structures on $D(U)$ for
all open $U\subset X$, are the perverse t-structures considered in
math.AG/0005152.

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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci