Coherent Sheaves: Locally Ringed Space

This lecture covers the definition of a locally ringed space, introducing the concept of coherent sheaves and their properties. The instructor explains the conditions for a sheaf to be quasi-coherent and the specialization to the case of schemes. The lecture delves into the notion of coherence in the context of algebraic geometry, emphasizing the importance of understanding the behavior of sheaves on schemes. Various examples and implications of coherent sheaves are discussed, highlighting their role in the study of locally Noetherian schemes.