In this talk I will discuss the torsion classes in the cohomology of SL_2(Z) as well as its variant with compact support.
As a consequence, we show how to deduce congruences of cuspidal forms with Eisenstein classes modulo small primes.
This generalizes the previous results on Ramanujan tau functions.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/246