Exponentiation of coefficient systems and exponential motives

Martin Gallauer; Simon Pepin Lehalleur

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arXiv · 2211.17247

Exponentiation of coefficient systems and exponential motives

Martin Gallauer·Simon Pepin Lehalleur

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Abstract

We construct new six-functor formalisms capturing cohomological invariants of varieties with potentials. Starting from any six-functor formalism $C$, encoded as a coefficient system, we associate a new six-functor formalism $C_{\text{exp}}$. This requires in particular constructing the convolution product symmetric monoidal structure at the $\infty$-categorical level. We study $C_{\text{exp}}$ and how it relates to $C$. We also define motives in $C_{\text{exp}}$ attached to varieties with potential and study their properties.

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Martin Gallauer, Simon Pepin Lehalleur. 2022-11-30. Exponentiation of coefficient systems and exponential motives. https://arxiv.org/abs/2211.17247

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