PvZ: how can Protoss keep up with the Zerg production?

A build order and correct macro is nearly all that you need to beat platinum players. 2base colossus and expand is usually pretty safe. Your third lands around 12 minutes. Immortals and colossus work much better than only gateway units, and they work well in conjunction with sentries ... which allows you to spend more minerals on a faster third, gates, pylons and other infrastructure

Repeatedly check for spire so that he doesn't kill you with mutas while you're making colossus.

Keep in mind, Stephano coined the 11 minute roach max ... so 133 supply at 12 minutes is not that big. You're making some kind of macro mistakes if you're only at 92 supply by 12 minutes. The only exception I can think of, is if you take a super early third base with gateway walls and cannons... this will slow down your supply gain a bit.

For anyone who says you need to be aggressive, or defensive, or warpin zealots ... There is no need to do any of this. Just take a timely third, max out, A-move to victory. Favor immortals over stalkers if he's got a mass of roaches

It depends what the zerg is doing. If they are expanding and worker-pumping, they are likely to have a small army. Tho it render them fragile early game, they can quickly get economic lead mid to late game. Usually this will mean they are extremely aggressive early game. Still, zerg is supposed to be aggressive, so to beat them you need to be aggressive yourself, or really defensive.

Early game you will likely see ling\roach combo from the zerg. Zealots are hard counter to lings, stalkers (if I remember correctly) outrange roaches, so have a reasonable amount of zealots, and have stalkers kill off roaches from the back. Keep in mind to actually protect stalkers, cause they are easily killed. If they go all ling, pump zealots but don't let them get surrounded, try facing the lings in a choke point, like a ramp. Best move there is to keep close to your base with some cannons, move out only when you think you've cleared the majority of zerg attack forces. Build as normal in base.

Protos air is some of the best mid game, you can choose to either go with phoenix to pick off queens, or void rays to be more aggressive. Either is good.

Have cannons near key structures, but don't overdo their numbers, two-three well placed cannons should be able to cover the majority of a base area.

What I found myself as an effective deterrent for Zerg pumping drones is early zealots pressure.

In order to achieve that you should not put much static defense and may be don't tech too much. Instead do 1 of following options:

1. take a 2nd expansion
2. put early pressure with zealots