@article{THESIS,
      recid = {12781},
      author = {Kountouridis, Iason},
      title = {On the Monodromy of Rational Singularities in Mixed  Characteristic},
      publisher = {University of Chicago},
      school = {Ph.D.},
      address = {2024-08},
      number = {THESIS},
      abstract = {We study the ramification on the cohomology of a smooth  proper surface $X$ in mixed characteristic, when $X$  degenerates to a surface over $\overline{\mathbb{F}}_p$  with rational singularities, with a focus on the case of  rational double points. We find that the associated  monodromy action of inertia depends on a formal affine  neighborhood of the singularity, and under sufficient  restrictions on characteristic $p$, it is tamely ramified  and generated by a conjugacy class representative of an  appropriate Weyl group related to the singularity. This  naturally extends to a similar monodromy characterization  of general rational singularities. Along the way we extend  to mixed characteristic some results of Brieskorn and  Slodowy concerning simultaneous resolutions of surface  singularities. We also compare our Weyl group actions to  certain Springer representations constructed by Borho and  MacPherson, via the notion of relative perversity as  developed by Hansen and Scholze.},
      url = {http://knowledge.uchicago.edu/record/12781},
      doi = {https://doi.org/10.6082/uchicago.12781},
}