Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher degree S-lemma and the stability of quadratic modules   In this work we will investigate a certain generalization of the so called
S-lemma in higher degrees. The importance of this generalization is, that it is
closely related to Hilbert's 1888 theorem about tenary quartics. In fact, if
such a generalization exits, then one can state a Hilbert-like theorem, where
positivity is only demanded on some semi-algebraic set. We will show that such
a generalization is not possible, at least not without additional conditions.
To prove this, we will use and generalize certain tools developed by Netzer
([Ne]). These new tools will allow us to conclude that this generalization of
the S-lemma is not possible because of geometric reasons. Furthermore, we are
able to establish a link between geometric reasons and algebraic reasons. This
will be accomplished within the framework of quadratic modules.

27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg