Abstract: Milnor Witt cycle modules are quadratic analogues of Rost cycle modules, which can be used to define Chow-Witt groups using elementary arithmetic operations on residue fields. We introduce Milnor Witt cycle modules over a base scheme and discuss their relations with the homotopy t-structure on the motivic stable homotopy category. This is a joint work with F. Déglise and N. Feld.
