Research report 2018 - Max Planck Institute for Mathematics
Topological periodic homology
Authors
Thomas; Nikolaus
Departments
Max-Planck-Institut für Mathematik, Bonn
Summary
It is a classical algebraic problem to study solutions of polynomial equations. Since this can be very hard, people have invented certain algebraic invariants, called cohomology theories, to get a qualitative picture. Crystalline cohomology is one of these cohomology theories which is especially important in counting solutions over finite fields. It is an algebraic invariant, but it has recently been possible to express crystalline cohomology in terms of a topological invariant - called topological periodic homology. This leads to natural generalizations, extensions and computations.