In an opamp differentiator, how does high gain produce oscillations?
Here I made a simple simulation in LTspice assuming Vin = 0V: 



And the output voltage looks like this:



And the frequency of this oscillation is equal to: 

$$F = \sqrt{F_T \times F_{RC}} = \sqrt{1MHz \times \frac{0.16}{10\textrm{nF} \times 10\textrm{k}\Omega}} \approx 40\textrm{kHz}$$ 

Adding a resistor in series with the capacitor may fix the circuit because now at high frequency the feedback network phase shift is 0 degrees.