Last modified date: <%+ tp.file.last_modified_date() %>
- Tags:
-
Refs:
- Yves André (CNRS), “On the canonical, fpqc and finite topologies: classical questions, new answers (and conversely)”. Princeton/IAS NT seminar.
- Links:
Yves André (CNRS), “On the canonical, fpqc and finite topologies: classical questions, new answers (and conversely)”
Reference: Yves André (CNRS), “On the canonical, fpqc and finite topologies: classical questions, new answers (and conversely)”. Princeton/IAS NT seminar.
-
What does it mean for an algebra to be faithfully flat over another algebra?
-
p-adic Hilbert functor: see Bhatt-Lurie.
- Use this to get “almost results”, then use prismatic cohomology techniques (where one has Frobenius) to remove the “almost”.
-
Extracting \(p\)th roots? Passing from \(k[g_1, \cdots, g_n]\) to \(k[g_1^{1/p}, \cdots, g_n^{1/p}]\), I think…
-
F-pure and strongly F-regular singularities are characteristic \(p\) analogs of log canonical and log terminal singularities in the minimal model program.
-
Tilting : pass from mixed characteristic to characteristic \(p\). Try to use simpler proofs/theorems from characteristic \(p\) situation.
- Going forward: some limiting process after inverting \(p\)..? Going backward: take Witt Vectors.
-
What properties of schemes descend along faithfully flat morphism? See EGA. However, what properties descend for the fpqc topology?
- What is a faithfully flat morphism?
-
See Faltings’ almost purity theorem.
-
Commutative algebra: see excellent regular domains, integral vs algebraic closures.
- See Cohen-Macaulay rings and modules
-
Can have \({\operatorname{fpqc}}\) coverings that are not fppf coverings.
-
What is a regular scheme?
-
Theorem: any finite covering of a regular scheme is an \({\operatorname{fpqc}}\) covering.
-
Very nontrivial in characteristic zero.
-
Noether normalization can show some finite coverings of \({\mathbf{A}}^3_{/k}\) are not \({\operatorname{fppf}}\) coverings.
-
-
Sometimes local or coherent cohomology classes
-
See Grothendieck’s descent?
faithfully flat implies something is an equivalence.