Iris.Shi

Affiliation: University of Florida

Title Of Talk: A T-adic computation of the Cartier operator

Abstract: The Cartier operator is dual to the Frobenius on H^1(X, O_X) via Serre duality, making it a key tool in the algorithmic study of curves over finite fields. For Artin-Schreier curves in characteristic p, computing the matrix of the Cartier operator on the space of regular differentials is a fundamental computational problem. In this talk, we introduce a T-adic method for computing the Cartier operator. This approach provides significant algorithmic improvements over the classical method of directly computing the image of each basis element. The T-adic method exploits p-adic analysis to reduce the computational complexity. We will compare various computational approaches and discuss their relative efficiency and implementation strategies.

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