ABSTRACT:
Cohomological tools: the Kummer sequence in ´etale cohomology and flat cohomology; relation to Milnor K-theory; logarithmic differentials; the de Rham–Witt complex.
Ramification: residues, Bloch–Kato filtration on K-theory, Kato’s Swan conductor.
Evaluating elements of the Brauer group: work of Yamazaki (1999) on curves in mixed characteristic; work of Bright-Newton (2023) on mixed characteristic in general.
Introduction to prismatic cohomology.
Work of Valloni (2025) on constructing elements of the Brauer group in characteristic p.
The lectures will offer some preparation for the talks of Majumder, Newton and Skorobogatov during the April workshop.
Schedule: 30th March, April 1st, April 3rd at 2.30PM.