Condensed Learning Seminar

Review the notion of cd-structure for a Grothendieck topology and explain how it helps check the sheaf conditions. Introduce and discuss the Nisnevich topology for schemes and analytic adic spaces; in particular, discuss their equivalent characterizations and describe the points of the corresponding topoi. Prove that the Nisnevich topology in both situations comes with a cd-structure. Using it, prove that nuclear sheaves satisfies Nisnevich descent on qcqs analytic adic spaces and deduce from it Nisnevich descent for localizing invariants. Sketch the proof of the fact that étale descent is Nisnevich+Galois and prove that nuclear sheaves satisfy étale descent.