Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analogy between the cyclotomic trace map $K \rightarrow TC$ and the
  Grothendieck trace formula via noncommutative geometry   In this article, we suggest a categorification procedure in order to capture
an analogy between Crystalline Grothendieck-Lefschetz trace formula and the
cyclotomic trace map $K\rightarrow TC$ from the algebraic $K$-theory to the
topological cyclic homology $TC$. First, we categorify the category of schemes
to the $(2, \infty)$-category of noncommuatative schemes a la Kontsevich. This
gives a categorification of the set of rational points of a scheme. Then, we
categorify the Crystalline Grothendieck-Lefschetz trace formula and find an
analogue to the Crystalline cohomology in the setting of noncommuative schemes
over $\mathbf{F}_{p}$. Our analogy suggests the existence of a categorification
of the $l$-adic cohomology trace formula in the noncommutative setting for
$l\neq p$. Finally, we write down the corresponding dictionary.

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The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci