- Info

# Zinovy Reichstein

### The University of British Columbia

### Two types of problems in algebra

Let p be a prime integer. I will say that a field extension L/K is prime-to-p if
the degree [L : K] is finite and not divisible by p. In this informal and mostly meta-mathematical
talk, I will discuss two types of problems concerning objects defined over fields K (such
as algebras, homogeneous polynomials, algebraic varieties, etc.) I will refer to problems that
are insensitive to prime-to-p extensions as "Type 1" and those that are as "Type 2". Many problems
can be naturally subdivided into "Type 1" and a "Type 2" components. My main observation is
that virtually all of the tools we have at our disposal are capable of proving Type 1 theorems
only, while many of the long-standing open problems are of Type 2. I discuss multiple examples
illustrating this philosophy.