Work

Quadratically enriched binomial coefficients over a finite field

Year: 2026

Type: other

Abstract: We compute an analogue of Pascal’s triangle enriched in bilinear forms over a finite field. This gives an arithmetically meaningful count of the ways to choose j j ring homomorphisms into an algebraic closure from an étale extension of degree n n . We also compute a quadratic twist. These (twisted) enriched binomial coefficients are defined in joint work of Brugallé and the second-named author, building on work of Serre. Such binomial coefficients support curve counting results over non-algebraically closed fields, using A 1 \mathbb {A}^1 -homotopy theory.

Source: Contemporary mathematics - American Mathematical Society

DOI: 10.1090/conm/842/16851

Authors: Chongyao Chen, Kirsten Wickelgren

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: A1-Homotopy Theory and Applications to Enumerative Geometry and Number Theory, Motivic Homotopy Theory and Applications to Enumerative Geometry, Complex Geometric Properties of Period Maps

OpenAlex ID: W4405627334

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