### Journal Club – Geometric Infinity-Function Theory – Week 4

#### Posted by Urs Schreiber

In our journal club on [[geometric $\infty$-function theory]] this week Chris Brav talks about chapter 4 of *Integral Transforms*:

*Tensor products and integral transforms*.

This is about tensoring and pull-pushing $(\infty,1)$-categories of quasi-coherent sheaves on perfect stacks.

Luckily, Chris has added his nice discussion right into the wiki entry, so that we could already work a bit on things like further links, etc. together. Please see section 4 here.

Discussion on previous weeks can be found here:

week 1: Alex Hoffnung on *Introduction*

week 2: myself on *Preliminaries*

week 3: Bruce Bartlett *Perfect stacks*

## Re: Journal Club – Geometric Infinity-Function Theory – Week 4

Thanks Chris, elegantly written. Some quick questions for anyone out there, also posted on the nLab.

where $\overline{X}$ refers to the complex manifold $X$ equipped with the ‘conjugate charts’… is this right? I’m not sure if $X \cong \overline{X}$ for complex manifolds in general (maybe I’m just being dense here). So the self-dual step doesn’t go through in this setting. On the other hand, in the perfect stack situation everything is nicely self-dual. How come?