Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative singular locus and Balmer spectrum of matrix factorizations   For a separated Noetherian scheme $X$ with an ample family of line bundles
and a non-zero-divisor $W\in\Gamma(X,L)$ of a line bundle $L$ on $X$, we
classify certain thick subcategories of the derived matrix factorization
category ${\rm DMF}(X,L,W)$ of the Landau-Ginzburg model $(X,L,W)$.
Furthermore, by using the classification result and the theory of Balmer's
tensor triangular geometry, we show that the spectrum of the tensor
triangulated category $({\rm DMF}(X,L,W), \otimes^{\frac{1}{2}})$ is
homeomorphic to the relative singular locus ${\rm Sing}(X_0/X)$, introduced in
this paper, of the zero scheme $X_0\subset X$ of $W$.

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th