Berkovich analytification and tropicalization of smooth algebraic curves, and tropical algebraic curves

Time:

Venue/Location: Phòng C101, VIASM, 157 phố Chùa Láng, Hà Nội

Báo cáo viên: Cristhian Emmanuel Garay Lopez, Center for Research in Mathematics, Mexico

Tóm tắt: Analytification is a very important tool in complex algebraic geometry. At a very basic level, it improves the topology of our complex algebraic varieties, but it is also available for sheaves. It turns out that this process can also be performed for algebraic varieties over other fields once we equip them with a rank 1 valuation. In this talk, we will describe how to do this process for smooth algebraic curves defined over a non-Archimedean field, which is a case that is well-understood. After that, we will discuss how the tropicalization process enters into the picture once we embed our curves inside a toric variety.