This embedded 10-minute Youtube video contains the core ideas:
https://www.youtube.com/watch?v=BfITeN76Thc

Notes:

- Warm air naturally moves up, and cool air naturally moves down. A chimney is like a hot air balloon

- The taller the chimney, the faster the smoke rises. Exponentially.

- The temperature drops 10 C every 1000 meters we go up. This is because there is more heat at the ground than in the sky (Transcriber's note: Dense air at the surface can store more heat than thin air near space can.)

- Consider a 5km chimney - the air at the base will be 50c warmer than at the top. This will cause dramatic airflow, up to 300 mph. While the air inside will be like the air outside, it will be hotter inside, due to the lack of Adiabatic cooling. When air rises, it pushes on the air it's passing, causing it to exchange heat with the air it's passing.

- By contrast, the chimney compresses air and causes it to gain heat and rush up, cooling the chimney.

- When warm air exits the top, the hot air causes precipitation in the cool air it's entering. AKA sudden clouds for deserts, or Oasis_aaS.

- Deserts are ideal, as they allow year-round operation. (Transcriber's note: Does that mean the ground and the upper atmosphere are less than 50C difference in northern areas?)

- The rains will cause carbon fixing, as more plants consume it and biodegrade into dirt.

- Global warming isn't caused by the planet receiving more heat, but by the planet storing more heat. (Transcriber's note: As an amateur astronomer, I disagree slightly. Part of the problem is how even our orbit is, which will change over the next 100,000 years.)

- This is basically a heat pump for the planet, like a reverse hurricane.

- There's less atmosphere between the upper atmosphere and space, than there is between the surface and space, so more heat will be radiated away by the air in this way. And the thinner atmosphere will reabsorb less of that heat than the denser atmosphere near the surface would.

- The chimney will be suspended entirely by the buoyancy of the air leaving it - it will have a "mushroom cap" which will direct exiting air downward, to push the chimney upward.

- They're expecting to use Hot Air Balloon fabric, and that it will be sturdy enough to be 3 miles (5 kilometers, 1640 story building) tall, and withstand winds and other shearing forces.

- Close the mushroom caps, and use hot air balloons, during initial inflation; then open the mushroom caps once it's fully inflated.

- 20 meter diameter chimney is estimated to cost ~ $5000.

- 25k super chimneys needed to completely address global warming, estimated cost $125,000,000.

- Total global economy estimated at $71,277,000,000,000, so this is a 0.17% global GDP investment opportunity. (Transcriber's note: IANAL nor fiduciary.)

There's a table included too, it's not easy to reproduce:

Height m - 2000 - 3000 - 4000 - 5000 - 5000 - 5000 -
Diameter m - 500 - 500 - 700 - 1000 - 10 - 20 -
Air Temperature at the base ?C - 30 - 30 - 30 - 30 - 30 - 30 -
Air Temperature at the upper end ?C - 10 - 0 - -10 - -20 - -20 - -20 -
Air Speed m/s - 52.7 - 80.4 - 109.2 - 139 - 139 or 500km/h or 300mph - 139 or 500km/h or 300mph -
Air Flow kg/s - 12,034,838 - 18,379,911 - 48,938,418 - 127,292,000 - 12,729 - 50,916 -
Producing electric power Mega Watt - 4447 - 15790 - 77542 - 327,786 - 32.8 - 131.1 -
amount of water condensate/precipitation kg per second - 0 - 73,520 - 327,887 - 929,231 - 93 - 371 -
CO2 uptake by irrigated desert tons - 0 - 147835 - 946,146 - 1,478,354 - 148 - 592 -
number of super-chimneys needed to cool the atmosphere - 224 - 99 - 27 - 10 - 100,000 - 25,000

Edits complete.