## Standard conjecture of Künneth type with torsion coefficients

Junecue Suh

University of California, Santa Cruz

April 21, 2016

A. Venkatesh asked us the question, in the context of torsion automorphic forms: Does the Standard Conjecture (of Grothendieck's) of Künneth type hold with mod p coefficients? We first review the geometric and number-theoretic contexts in which this question becomes interesting, and provide answers: No in general (even for Shimura varieties) but yes in special cases.