I'm currently taking a class on modular forms, and I'm doing a presentation on how you can write the space of modular forms with coefficients in a $K$-algebra $A$ as the group cohomology ring $H^{1}(\operatorname{SL}_{2}(\mathbb{Z}),\Omega^1_{A/K})$ where $\Omega^1_{A/K}$ is the space of Kähler $K$-differentials on $A$. However, I cannot seem to find any references for this fact, and I was just wondering if anyone knew of any references where I can find this fact, or places where I can find stuff related to this? Thanks in advance!

  • 2
    $\begingroup$ It's not Kähler derivations but differentials, no? $\endgroup$ Jan 19, 2018 at 16:47
  • $\begingroup$ @MarianoSuárez-Álvarez You are correct, and thank you for the correction! Morning math is not my friend. $\endgroup$
    – Geoff
    Jan 19, 2018 at 18:43


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