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Singularities and vanishing cycles in number theory over function fields

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Abstract

This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example and then give three examples which are relevant to current research. The focus will be a general explanation of which sorts of problems this method can be applied to.

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Acknowledgements

This article was written while the author served as a Clay Research Fellow. I would like to thank Johan de Jong, Jordan Ellenberg, Philippe Michel, and (especially) the anonymous referee for many helpful comments on earlier versions of this paper.

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  1. Columbia University, New York, NY, USA

    Will Sawin

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Sawin, W. Singularities and vanishing cycles in number theory over function fields. Res Math Sci 7, 12 (2020). https://doi.org/10.1007/s40687-020-00210-x

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