An arithmetic topos for integer matrices

@article{Hemelaer2018AnAT,
  title={An arithmetic topos for integer matrices},
  author={Jens Hemelaer},
  journal={Journal of Number Theory},
  year={2018},
  volume={204},
  pages={155-184}
}
Abstract We study the topos of sets equipped with an action of the monoid of regular 2 × 2 matrices over the integers. In particular, we show that the topos-theoretic points are given by the double quotient GL 2 ( Z ˆ ) \ M 2 ( A f ) / GL 2 ( Q ) , so they classify the groups Z 2 ⊆ A ⊆ Q 2 up to isomorphism. We determine the topos automorphisms and then point out the relation with Conway's big picture and the work of Connes and Consani on the Arithmetic Site. As an application to number theory… Expand

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References

SHOWING 1-10 OF 36 REFERENCES
The skew-growth function on the monoid of square matrices
Noncommutative Geometry of Groups Like Γ0(N)
Noncommutative geometry of groups like $\Gamma_0(N)$
The Arithmetic Site
Some Common Tor and Ext Groups
  • 2009
The Monstrous Moonshine Picture
Principal ideals in matrix rings
The Riemann-Roch strategy, Complex lift of the Scaling Site
...
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2
3
4
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