Talk 1 (Colloquium)
Speaker : Rakesh Pawar
Title: Milnor-Witt cycle modules over excellent DVR
Date, Time, Venue : 4:00 pm on Wednesday (31st July) in Ramanujan Hall
Abstract: I will briefly recall Cycle modules over a field as defined by
Rost (1996) and their significance and properties. Recently, 'modules'
over Milnor-Witt K-theory or alternatively Milnor-Witt cycle modules
over field have been formalized by N. Feld (2020).
I will talk about recent joint work with Chetan Balwe and Amit Hogadi,
where we considered the Milnor-Witt cycle modules over excellent DVR and
studied a subclass of these that satisfy certain lifting conditions on
residue maps associated with horizontal valuations. As an important
example, Milnor-Witt K-theory of fields belongs to this subclass.
Moreover, this condition is sufficient to deduce the local acyclicity
property and A^1-homotopy invariance of the associated Gersten complex.