On the formal arc space of a reductive monoid

@article{Bouthier2016OnTF,
  title={On the formal arc space of a reductive monoid},
  author={A. Bouthier and A. B. C. Y. Ng{\^o} and A. Sakellaridis},
  journal={American Journal of Mathematics},
  year={2016},
  volume={138},
  pages={108 - 81}
}
Let $X$ be a scheme of finite type over a finite field $k$, and let ${\cal L} X$ denote its arc space; in particular, ${\cal L} X(k)=X(k[[t]])$. Using the theory of Grinberg, Kazhdan, and Drinfeld on the finite-dimensionality of singularities of ${\cal L} X$ in the neighborhood of non-degenerate arcs, we show that a canonical ``basic function'' can be defined on the non-degenerate locus of ${\cal L} X(k)$, which corresponds to the trace of Frobenius on the stalks of the intersection complex of… Expand

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