Capacitors, ground between connection, Colpitts oscillator
In terms of oscillation frequency analysis you can just concentrate on the oscillating AC current entering ground from one capacitor and leaving ground and entering the other capacitor. The fact that it uses ground is of no importance. For instance, that common net could connect to ground via a large value capacitor and that would not make any difference to the result; the AC current from one capacitor will still be largely the AC current of the other capacitor.

The oscillation frequency will still be this: -

$$\omega = \sqrt{\dfrac{C_1+C_2}{L\cdot C_1\cdot C_2}}$$

And if you analyse the formula you will see that the effective capacitance is the series combination of C1 and C2. However, I believe that many authors miss the whole point of how the colpitts oscillator works and are too quick to state that the two capacitors are in series (basing this conclusion on the formula for the oscillating frequency). It's subtler than that.

My personal choice (should I have written an article on the colpitts oscillator) is to not confuse the issue but just derive the oscillation frequency on the basis that there are two phase shifting networks in series.

The first phase shift comes from R1 and C1 and the 2nd phase shift comes from L1 and C2. Here's an extract of the derivation and note that this derivation just regards ground as ground: -



And, in the final analysis, the oscillation frequency happens to have a formula that can be re-written to imply C1 is in series with C2 (but that is somewhat missing the point because it's the phase shift that matters and it's a 0 deg phase shift that dictates the oscillation frequency).

That final oscillation frequency formula also disguises the fact that R1 plays a significant role in determining the phase shift BUT, its value happens to get cancelled out in the algebra. It doesn't mean that a colpitts oscillator can work with R1 = 0, it means that R1 can be a range of values.