Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hilbert-Kunz criterion for solid closure in dimension two
  (characteristic zero)   Let I denote a homogeneous R_+-primary ideal in a two-dimensional normal
standard-graded domain over an algebraically closed field of characteristic
zero. We show that a homogeneous element f belongs to the solid closure I^* if
and only if e_{HK}(I) = e_{HK}((I,f)), where e_{HK} denotes the (characteristic
zero) Hilbert-Kunz multiplicity of an ideal. This provides a version in
characteristic zero of the well-known Hilbert-Kunz criterion for tight closure
in positive characteristic.

16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom