The Yagita invariant of symplectic groups of large rank

TL;DR

This paper computes the Yagita invariant at a prime p for symplectic groups of large rank over certain rings, extending understanding of their algebraic properties.

Contribution

It provides explicit calculations of the Yagita invariant for symplectic groups over rings with specific properties, for all ranks n ≥ p-1.

Findings

Yagita invariant computed for all n ≥ p-1

Results apply to rings containing a primitive pth root of unity or being integrally closed

Advances the understanding of symplectic group invariants at prime p

Abstract

Fix a prime $p$, and let $R$ be any subring of the complex numbers that is either integrally closed or contains a primitive $p$th root of 1. For each $n\geq p-1$ we compute the Yagita invariant at the prime $p$ for the symplectic group $Sp(2n,R)$.