# Speaker
Matthias Hutzler

# Title
Projective Space and Line Bundles in Synthetic Algebraic Geometry

# Abstract

Synthetic algebraic geometry interprets HoTT as internal language for (a higher
topos version of) the Zariski topos. This means that schemes such as projective
space appear simply as certain h-sets without any added structure. In the talk
we present a synthetic version of the classical classification result for line
bundles on projective space. The language of HoTT allows us to give a stronger
variant of the classical statement, describing the 1-type of line bundles
instead of its set-truncation, the Picard group. This is used to give a proof
that requires nontrivial algebraic arguments only for the case of the projective
line, and derives the general case by an interpolation argument.