Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of locally-closed semi-algebraic subsets   Let k be a non archimedean field. If X is a k-algebraic variety and U a
locally closed semi-algebraic subset of X^{an} -- the Berkovich space
associated to X -- we show that for l \neq char(\tilde{k}), the cohomology
groups H^i_c (\bar{U}, Q_l) behave like H^i_c(\bar{X}, Q_l), where \bar{U} = U
\otimes \hat{\bar{k}}. In particular, they are finite-dimensional vector
spaces. This result has been used by E. Hrushovski and F. Loeser. Moreover, we
prove analogous finiteness properties concerning rigid semi-analytic subsets of
compact Berkovich spaces (resp. adic spaces associated to quasi-compact
quasi-separated k-rigid spaces) when char(\tilde{k}) \neq 0 (resp in any
characteristic).

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The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci