Here are the texed notes for my 1 hour oberwolfach talk (the key thing I left out is Cartier duality). I included Manin’s original approach, and remark on some details I find left out of most sources.
officialoberIf the pdf viewer doesn’t work, here is a link to the paper.
Beauty wilts
and love will flucture
what remains
is hidden structure
blushing primes
sly chiding knots
intertwine
betwixt our thoughts
creation
lives to create
chipping from
the ob’lisk slate
talk amoungst
our little selves
speculating
filling shelves
search we will
and see we’ll not
blindness is
our earthly lot
but the voice
of the void is vast
notice it
through the nets we cast
Read our arxiv paper: https://arxiv.org/abs/1811.07007
Here, $A$ is any abelian variety. This post consists of the backstory of this paper, and something interesting I learned about the relationship between the size of $Aut(A)$, and the number of principal polarizations $A$ has. Continue reading Automorphisms of the Jacobian
Here is an incomplete proof that varieties are fiber bundles of formal disks over their deRham Stacks. The fact makes intuitive sense, the deRham stack is the variety without infinitesimal data, and then by adding the infinitesimal data (formal disks) back in, you recover the result. However, the fact that you can build anything non infinitesimal out of formal disks fills me with confusion and awe.
Acknowledgements: This is the result of a working group with Dan Fletcher, Adam Holeman, and me as part of the Northwestern Homotopy Working Seminar (started by Matthew Weatherly, Grigory Kondyrev, and me). The working session in which Adam and I figured out the proof, Dan was not there, which is why his name is not mentioned, but he was very helpful in understanding the claim. This proof is the result of Yaroslav Khromenkov coming up with the idea of it, and Adam and I understanding and correcting his solution during a working session.
formalgroupIf the pdf viewer doesn’t work, here is a link to the paper.
