Yves Andre has proved the direct summand conjecture, using perfectoid methods.

**Update (Sept. 7): **Andre’s paper is here, and Bhatt’s shorter proof is here.

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## Rumor of the week

## Arithmetische geometrie

## Autocorrect doesn’t know math

## Hodge-Newton paradise

## Moron

Yves Andre has proved the direct summand conjecture, using perfectoid methods.

**Update (Sept. 7): **Andre’s paper is here, and Bhatt’s shorter proof is here.

Just attended a week-long meeting at Oberwolfach on arithmetic geometry.

- “So did you do this computation like Gauss, or did you use a computer?” – Gabber to Katz

- “Let the indices work it out themselves!” – Janssen

- “Shouwu, either you’re going to answer my question, or I’m going to hand you over to Ofer!” – Kisin

- Katz (telling a story at the beginning of his talk): “… So anyway, after Spencer returned to Princeton, this is how he described the math department at Stanford [where he had just been a professor for a couple years]: ‘At Stanford, they’re still studying the topology of the unit disk!’ ”

Conrad (from the audience): “Those days are over.”

- “We use what I wrote.” – Janssen reassuring Gabber

- “So Peter, why did you turn down the breakthrough prize? [pause] I’m only asking because I’m drunk!”

- Anon.: “So Ofer, do you come here much?”

Gabber: [looks down at table, silently moves his finger across it in stepwise motion for 30 seconds] “Seventeen times.”

- Two common referees for technical papers on Shimura varieties: Frobenius and Verschiebung.

- Me (after writing down the “new” definition of a diamond): “Is that OK, Peter?”

Scholze (from the back row): “Looks good!”

- Zhang: “So Mochizuki is like the Buddha. He writes his ideas. He is satisfied. If you want to understand them, you visit him, you ask him questions, he gives you a little idea, you go away and study. You have to be a monk. Have a monk’s approach.”

Anon.: “Unfortunately, there aren’t very many good monks.”

- A “symplectic lifting whatever shit”. Apparently they’re defined in Kai-Wen Lan’s thesis?

- Gabber was NOT happy when he heard about Mochizuki’s Gaussian integral analogy.

- While eating the horrible bread casserole thing, which Kedlaya, Lieblich and I had mangled pretty badly while serving ourselves:

Lieblich:”What is this supposed to BE?”

Kedlaya: “Some kind of croque madame?”

Nizioł: “Yes, a croque madame. But I think you guys croqued it.”

The autocorrect feature in Gmail has the unfortunate but hilarious habit of vigorously changing standard math terms into free-associative nonsense. Here are some highlights (and I might add to this list from time to time):

- “Igusa varieties” -> “Iguana varieties”
- “Zariski topology” -> “Czarist topology”
- “Gelfand spectrum” -> “Gelatin spectrum”
- “cokernel” -> “cockerel” (my favorite so far)

I just posted a new version of my preprint on local shtukas and Harris’s conjecture. To be clear, the goal of this paper is to make good on the optimism I expressed in this previous post. This project has been one of the most intense mathematical experiences of my life, and I hope to write a proper blog post about it soon.

Anyway, the paper should basically be stable at this point, with the exception that will probably be rewritten to some degree once Peter’s six-functors book is done. The only real difference from the the first version is that the material around the “pointwise criterion” in has been streamlined and clarified a bit. All comments, questions or corrections are very welcome!

OK, this blog is a continuation of my original blog. Long story short, I set up arithmetica many years before I started posting there, using an email address I no longer have access to, and I recently lost/messed up the password. Won’t make that mistake again.