Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagonal forms of higher degree over function fields of $p$-adic curves   We investigate diagonal forms of degree $d$ over the function field $F$ of a
smooth projective $p$-adic curve: if a form is isotropic over the completion of
$F$ with respect to each discrete valuation of $F$, then it is isotropic over
certain fields $F_U$, $F_P$ and $F_p$. These fields appear naturally when
applying the methodology of patching; $F$ is the inverse limit of the finite
inverse system of fields $\{F_U,F_P,F_p\}$. Our observations complement some
known bounds on the higher $u$-invariant of diagonal forms of degree $d$. We
only consider diagonal forms of degree $d$ over fields of characteristic not
dividing $d!$.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga