Exponential sums on 𝐀ⁿ, II

Adolphson, Alan; Sperber, Steven

doi:10.1090/S0002-9947-03-03324-5

Exponential sums on $\mathbf {A}^n$, II
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by Alan Adolphson and Steven Sperber

Trans. Amer. Math. Soc. 356 (2004), 345-369

DOI: https://doi.org/10.1090/S0002-9947-03-03324-5

Published electronically: May 29, 2003

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Abstract:

We prove a vanishing theorem for the $p$-adic cohomology of exponential sums on $\mathbf {A}^n$. In particular, we obtain new classes of exponential sums on $\mathbf {A}^n$ that have a single nonvanishing $p$-adic cohomology group. The dimension of this cohomology group equals a sum of Milnor numbers.

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