Takeshi Torii

## Power operations and the generalized Chern character

video: comming soon.
abstract:
We have defined a generalization of the Chern character as a multiplicative natural transformation from the $$(n+1)$$st Morava $$E$$-theory to a certain extension of the $$n$$th Morava $$E$$-theory, which we call the generalized Chern character. On the other hand, we have power operations in Morava $$E$$-theory, since it is an $$E_{\infty}$$-ring spectrum. In this talk I will discuss the relationship between power operations in different Morava $$E$$-theories through the generalized Chern character.