  We generalize the concept of rigid inner forms, defined by Kaletha in
[Kal16], to the setting of a local function field $F$ in order state the local
Langlands conjectures for arbitrary connected reductive groups over $F$. To do
this, we define for a connected reductive group $G$ over $F$ a new cohomology
set $H^{1}(\mathcal{E}, Z \to G) \subset H_{\text{fpqc}}^{1}(\mathcal{E}, G)$
for a gerbe $\mathcal{E}$ attached to a class in $H_{\text{fppf}}^{2}(F, u)$
for a certain canonically-defined profinite commutative group scheme $u$,
building up to an analogue of the classical Tate-Nakayama duality theorem. We
define a relative transfer factor for an endoscopic datum serving a connected
reductive group $G$ over $F$, and use rigid inner forms to extend this to an
absolute transfer factor, enabling the statement of endoscopic conjectures
relating stable virtual characters and $\dot{s}$-stable virtual characters for
a semisimple $\dot{s}$ associated to a tempered Langlands parameter.
