Date:

Mon, 20/06/202214:30-16:00

Title: "Non-archimedean pinchings"

In my talk I'll outline the classical theory of the so-called Ferrand's pushouts of schemes. In particular, this class includes

pinchings of a scheme along a finite morphism from its closed subscheme. After that I will tell about my recent work on

pinchings in the category of non-archimedean spaces (rigid, Berkovich or adic). Surprisingly, the theory is more complicated

in the local (i.e. affinoid) case -- a pinching does not have to be affinoid, but is nicer in the global case -- no need to consider

rigid analogs of algebraic spaces. In particular, we will see a conceptual explanation of the strange phenomenon that

there exist non-affinoid spaces whose normalization is affinoid.

In my talk I'll outline the classical theory of the so-called Ferrand's pushouts of schemes. In particular, this class includes

pinchings of a scheme along a finite morphism from its closed subscheme. After that I will tell about my recent work on

pinchings in the category of non-archimedean spaces (rigid, Berkovich or adic). Surprisingly, the theory is more complicated

in the local (i.e. affinoid) case -- a pinching does not have to be affinoid, but is nicer in the global case -- no need to consider

rigid analogs of algebraic spaces. In particular, we will see a conceptual explanation of the strange phenomenon that

there exist non-affinoid spaces whose normalization is affinoid.