On even $K$-groups over $p$-adic Lie extensions of global function fields

TL;DR

This paper investigates the growth patterns of Sylow p-subgroups in even K-groups over p-adic Lie extensions of global function fields, establishing duality relations and extending understanding of algebraic K-theory in this context.

Contribution

It introduces new results on the growth of even K-groups in p-adic Lie extensions of function fields and establishes a duality between their direct and inverse limits.

Findings

Growth patterns of Sylow p-subgroups characterized.

Duality between direct and inverse limits established.

Extension of algebraic K-theory results to function fields.

Abstract

Let $p$ be a fixed prime number, and $F$ a global function field of characteristic not equal to $p$. In this paper, we shall study the growth of the Sylow $p$-subgroups of the even $K$-groups in a $p$-adic Lie extension of $F$, where the $p$-adic Lie extension is assumed to contain the cyclotomic $\mathbb{Z}_p$-extension of $F$. We also establish a duality between the direct limit and inverse limit of the even $K$-groups.