ABC Day 4

The play showing today at the Hodge Theatre was a farce.

Yesterday there was some optimism that something concrete would happen today, starting from the result that Kedlaya explained. Namely,  that the valuation of the discriminant of an elliptic curve of  bad reduction could be obtained by group theory from the tempered fundamental group of the affine curve obtained by deleting the origin from the curve over a local field. Today, Kedlaya started by tidying up some technical details from yesterday.

Mok then gave an one hour lecture with motivations for what would came next, which didn't help me. He then started with Hodge theaters and it was another barrage of definitions without clear purpose. These seem to be collections of interlinked categories of various sorts. They are attached to the affine curve X obtained by deleting the origin from an elliptic curve over a number field and contain at least the etale fundamental group of X at the good places, the tempered fundamental group of X at the bad places and whatever comes out of TAAG III Cor 4.5 (which nobody understood Tuesday) at the ugly, er archimedian, places. It also had some information about the ground number field but I didn't get that. The talk also suffered from bad scheduling and unfortunate computer problems. I found the general cluelessness humorous but Fesenko was not amused.

At the afternoon tea break, everybody was confused. I asked many people and nobody had a clue.

After that, Hoshi gave a very technical talk about Hodge theaters, etale theta functions and the mysterious theta link but I was too exhausted to follow.

Unfortunately, the optimism from the morning had dissipated in the afternoon and the energy was gone from the room. The crowd was unusually quiet. Tomorrow we have four hours of Yamashita plus a Skype session with Mochizuki. I don't know what to expect.
Shared publiclyView activity