Title：Higher amalgamation in PAC fields

Speaker：Nick Ramsey (University of Notre Dame)

Time: 2024/06/03 14:00-15:00

Zoom room: 717 463 6082

Organizer: Kyle Gannon (BICMR)

Abstract：

　　Pseudo algebraically closed (PAC) fields, introduced by Ax in his characterization of pseudo-finite fields, are an important class of examples in both model theory and field arithmetic.  A recurrent theme in the study of PAC fields is that their analysis often reduces to an analysis of the absolute Galois group.  One of the most significant results along these lines is a theorem of Chatzidakis, which relates the independence theorem in a PAC field to the independence theorem in the inverse system of the absolute Galois group, viewed as a first-order structure.  We explain how this connection can be generalized to relate independent n-amalgamation in a PAC field to independent n-amalgamation in the absolute Galois group.  We will describe some corollaries for omega-free PAC fields and, more generally, for Frobenius fields.