Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple algebraic groups with the same maximal tori, weakly commensurable
  Zariski-dense subgroups, and good reduction   We provide a new characterization of the existence of good reduction for an
absolutely almost simple algebraic group with respect to a discrete valuation
of the base field that is formulated in terms of the existence of maximal tori
with special properties. This characterization, in particular, shows that the
Finiteness Conjecture for forms of an absolutely almost simple algebraic group
over a finitely generated field that have good reduction at a divisorial set of
places of the field would imply the finiteness of the genus of the group at
hand. It also leads to a new phenomenon that we refer to as "killing of the
genus by a purely transcendental extension." Yet another application deals with
the investigation of "eigenvalue rigidity" of Zariski-dense subgroups, which in
turn is related to the analysis of length-commensurable Riemann surfaces and
general locally symmetric spaces. Finally, we analyze the genus problem for
simple algebraic groups of type $\textsf{F}_4$.

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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th