In mathematics, the flat topology is a Grothendieck topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also plays a fundamental role in the theory of descent (faithfully flat descent). The term flat here comes from flat modules. There are several slightly different flat … See more Let X be an affine scheme. We define an fppf cover of X to be a finite and jointly surjective family of morphisms (φa : Xa → X) with each Xa affine and each φa flat, finitely presented. … See more The procedure for defining the cohomology groups is the standard one: cohomology is defined as the sequence of derived functors of the functor taking the sections See more • fpqc morphism See more • Arithmetic Duality Theorems (PDF), online book by James Milne, explains at the level of flat cohomology duality theorems originating in the Tate–Poitou duality of Galois cohomology See more Let X be an affine scheme. We define an fpqc cover of X to be a finite and jointly surjective family of morphisms {uα : Xα → X} with each Xα affine and each uα flat. This generates a pretopology: For X arbitrary, we define an fpqc cover of X to be a family {uα : Xα … See more The following example shows why the "faithfully flat topology" without any finiteness conditions does not behave well. Suppose X is the affine line over an algebraically closed field k. For each closed point x of X we can consider the local ring Rx at this … See more 1. ^ "Form of an (algebraic) structure", Encyclopedia of Mathematics, EMS Press, 2001 [1994] 2. ^ SGA III1, IV 6.3. 3. ^ SGA III1, IV 6.3, Proposition 6.3.1(v). 4. ^ *Grothendieck, Alexander; Raynaud, Michèle (2003) [1971], Revêtements étales et groupe … See more
[PDF] Selmer groups as flat cohomology groups Semantic Scholar
WebSELMER GROUPS AS FLAT COHOMOLOGY GROUPS PHDTHESISOFKĘSTUTISČESNAVIČIUS Abstract. Given a prime number p, Bloch and … WebUsing Cohomology, Lemma 20.17.1 in (1) is allowed since is flat by Morphisms, Lemma 29.25.8. Having said this, part (1) follows from part (2). Namely, part (1) is local on and … grep -wf a.txt b.txt c.txt
ag.algebraic geometry - 1st-flat cohomology group for elliptic …
WebEtale Cohomology (PMS-33) - Feb 08 2024 One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced tale cohomology in order to extend the ... basic properties of flat and tale morphisms and of the algebraic … WebPurity for flat cohomology Kestutis Cesnavicius, Peter Scholze Comments: 84 pages; slightly strengthened the main purity result and added sections about further properties of flat cohomology: adic continuity and adically faithfully flat descent; numerous smaller changes Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT) WebApr 13, 2024 · where \text {Ric}_g and \text {diam}_g, respectively, denote the Ricci tensor and the diameter of g and g runs over all Riemannian metrics on M. By using Kummer-type method, we construct a smooth closed almost Ricci-flat nonspin 5-manifold M which is simply connected. It is minimal volume vanishes; namely, it collapses with sectional … grep: warning: stray before