Periodic topological cyclic homology and the Hasse-Weil zeta function

@inproceedings{Hesselholt2016PeriodicTC,
  title={Periodic topological cyclic homology and the Hasse-Weil zeta function},
  author={Lars Hesselholt},
  year={2016}
}
We propose a definition of periodic topological cyclic homology and show that, for schemes smooth and proper over a finite field, the infinite dimensional cohomology theory that results provides a natural vessel for Deninger's cohomological interpretation of the Hasse-Weil zeta function by regularized determinants. In this way, the theory may be seen as a non-archimedean analogue of the cohomological interpretation of the zeta function in the archimedean case in terms of cyclic homology given… CONTINUE READING

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