  We introduce the first geometric construction of codes in the sum-rank
metric, which we called linearized Algebraic Geometry codes, using quotients of
the ring of Ore polynomials with coefficients in the function field of an
algebraic curve. We study the parameters of these codes and give lower bounds
for their dimension and minimum distance. Our codes exhibit quite good
parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry
codes in the Hamming metric. Furthermore, our construction yields codes
asymptotically better than the sum-rank version of the Gilbert-Varshamov bound.
