Gauss--Heilbronn Sums and Coverings of Deligne--Lusztig Type Curves
Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima
TL;DR
This paper investigates Gauss--Heilbronn sums on Witt vectors and their relation to Deligne--Lusztig type curves, providing a detailed analysis of Frobenius slopes for specific cases.
Contribution
It introduces a new analysis of Gauss--Heilbronn sums on Witt vectors and determines Frobenius slopes for certain Deligne--Lusztig type curves.
Findings
Explicit Frobenius slopes for 3-typical Witt vectors of length two
Complete characterization of Gauss--Heilbronn sums in this setting
Connections between exponential sums and algebraic curves
Abstract
We study exponential sums on Witt vectors, known as Gauss--Heilbronn sums, and the curves whose Frobenius traces realize these sums via a Deligne--Lusztig type construction. For 3-typical Witt vectors of length two, we analyze Gauss--Heilbronn sums, from which we fully determine the Frobenius slopes of the associated curves.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry