Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Around the Thom-Sebastiani theorem   For germs of holomorphic functions $f : (\mathbf{C}^{m+1},0) \to
(\mathbf{C},0)$, $g : (\mathbf{C}^{n+1},0) \to (\mathbf{C},0)$ having an
isolated critical point at 0 with value 0, the classical Thom-Sebastiani
theorem describes the vanishing cycles group $\Phi^{m+n+1}(f \oplus g)$ (and
its monodromy) as a tensor product $\Phi^m(f) \otimes \Phi^n(g)$, where $(f
\oplus g)(x,y) = f(x) + g(y), x = (x_0,...,x_m), y = (y_0,...,y_n)$. We prove
algebraic variants and generalizations of this result in \'etale cohomology
over fields of any characteristic, where the tensor product is replaced by a
certain local convolution product, as suggested by Deligne. They generalize
arXiv:1105.5210. The main ingredient is a K\"unneth formula for $R\Psi$ in the
framework of Deligne's theory of nearby cycles over general bases. In the last
section, we study the tame case, and the relations between tensor and
convolution products, in both global and local situations.

32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys