Tubular neighborhoods of local models, 1

For zoom details contact Peter Scholze (scholze@mpim...)

In this series of two talks we will discuss our proof of "unibranchness" of
the v-sheaf local models of moduli of local shtukas introduced in [SW20]
and studied in [AGLR22]. When the local model is representable our proof
could be given without leaving the realm of schemes. The second talk will
explain this proof. Now, over p-adic local fields the local models are representable
only in special cases as discussed in [AGLR22]. In the first  talk we explain
the backstage ingredients that allow us to pretend our spaces are "representable"
when following the proof. The main new technical input is a comparison theorem
of "algebraic" nearby cycles for kimberlites.