Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some results from algebraic geometry over Henselian real valued fields   This paper develops algebraic geometry over Henselian real valued (i.e. of
rank 1) fields $K$, being a sequel to our paper about that over Henselian
discretely valued fields. Several results are given including: a certain
concept of fiber shrinking (a relaxed version of curve selection) for definable
sets, the canonical projection $K^{n} \times K\mathbb{P}^{m} \to K^{n}$ and
blow-ups of the $K$-points of smooth $K$-varieties are definably closed maps, a
descent property for blow-ups, a version of the Lojasiewicz inequality for
continuous rational functions and the theorem on extending continuous
hereditarily rational functions, established for the real and $p$-adic
varieties in our joint paper with J. Kollar. The descent property enables
application of desingularization and transformation to a normal crossing by
blowing up in much the same way as over the locally compact ground field. Our
approach applies quantifier elimination due to Pas.

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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph