Tropicalizations of locally symmetric varieties

Q: What type of study is this?

This is a Quantitative Study study.

Eran Assaf; Madeline Brandt; Juliette Bruce; Melody Chan; Raluca Vlad

doi:10.48550/arxiv.2505.10504

May 15, 2025Open Access

Tropicalizations of locally symmetric varieties

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Key Points

Tropicalizations enhance understanding of locally symmetric varieties and their cohomology.
The study examines level structures on the moduli space of abelian varieties, showing significant applications.
It also explores the special unitary case, highlighting interactions with arithmetic groups.
These findings may provide new insights into tropical geometry and algebraic geometry.

Implication

Rigorous analysis reveals links between tropicalizations and cohomology of moduli spaces, suggesting broader implications.

Abstract

This paper provides a rigorous study of tropicalizations of locally symmetric varieties. We give applications beyond tropical geometry, to the cohomology of moduli spaces as well as to the cohomology of arithmetic groups. We study two cases in detail: the case of level structures on the moduli space Ag of abelian varieties, and the special unitary case.

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Cite This Study

Assaf et al. (2025) studied this question.

synapsesocial.com/papers/68f163c79903599108abcbec https://doi.org/10.48550/arxiv.2505.10504

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Tropicalizations of locally symmetric varieties

Key Points

Implication

Abstract

Discussion

Cite This Study

Tropicalizations of locally symmetric varieties

Key Points

Implication

Abstract

Discussion

Cite This Study

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