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arXiv · 2601.09418

A note on toric periods in unramified families

Alexandros Groutides
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Abstract

Let $A$ be the algebra $\mathbb{C}[X_1^{\pm 1},X_2^{\pm 1}]$ and $Q(A)$ its quotient field. In this short article, we exhibit the correct normalization for the toric period on the parabolically induced unramified family over $Q(A)$, so that it behaves optimally under restriction to the parabolically induced unramified family over $A$. This answers a question raised by D. Prasad, and points towards potential generalizations to a broader unramified Gan-Gross-Prasad setting.

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Alexandros Groutides. 2026-01-14. A note on toric periods in unramified families. https://arxiv.org/abs/2601.09418

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