On the growth of even K-groups of rings of integers in p-adic Lie extensions

Let $p$ be an odd prime number. In this paper, we study the growth of Sylow $p$-subgroups even $K$-groups rings integers in a $p$-adic Lie extension. Our results generalize previous Coates and Ji-Qin, where they considered situation cyclotomic $\mathbb{Z}_p$-extension. method proof differs from these work. Their relies on explicit description certain Galois group via Kummer theory afforded by context $\mathbb{Z}_p$-extension, whereas our approach is considering Iwasawa cohomology groups with coefficients $\mathbb{Z}_p(i)$ for $i\geq 2$. We should mention that latter possible thanks to Quillen-Lichtenbaum Conjecture which now known valid works Rost-Voevodsky. also note allows us work more general extensions do not necessarily contain theoretical does apply. Along way, torsionness second Finally, give examples extensions, can have nontrivial $\mu$-invariants.