WitrynaX-module is free if it is isomorphic to a direct sum of copies of O X, and it is locally free if Xcan be covered by open sets U for which Fj U is a free O Xj U-module. In that case, the rank of F on such an open set is the number of copies of the structure sheaf needed; if Xis connected, the rank of a locally free sheaf is the same everywhere. WitrynaDefinition. A morphism of schemes : is called a Nisnevich morphism if it is an étale morphism such that for every (possibly non-closed) point x ∈ X, there exists a point y ∈ Y in the fiber f −1 (x) such that the induced map of residue fields k(x) → k(y) is an isomorphism.Equivalently, f must be flat, unramified, locally of finite presentation, and …

WEIL RESTRICTION FOR SCHEMES AND BEYOND

WitrynaLet be a projective variety (possibly singular) over an algebraically closed field of any characteristic and be a coherent sheaf. In this article, we define the determinant of such that it agrees with the classical … Witryna27 sie 2024 · Idea. A quasicoherent sheaf of modules (often just “quasicoherent sheaf”, for short) is a sheaf of modules over the structure sheaf of a ringed space that is locally presentable in that it is locally the cokernel of a morphism of free modules.. For comparison, by the Serre-Swan theorem a vector bundle on a suitable ringed space is … heartland mallard m301

Vector bundles and locally free sheaves. We will often use the ...

Witryna8 kwi 2024 · Let G be a reductive group scheme over the p-adic integers, and let $$\\mu $$ μ be a minuscule cocharacter for G. In the Hodge-type case, we construct a functor from nilpotent $$(G,\\mu )$$ ( G , μ ) -displays over p-nilpotent rings R to formal p-divisible groups over R equipped with crystalline Tate tensors. When R/pR has a p … Witryna1 ‫ תשע"ו‬,‫כא בתשרי‬ A abbreviate )‫ְמקַ צֵּ ר (פִ ע‬ Abel )‫אַ בֵּּ ל (שם פרטי‬ Abel summation ‫סְ כִ ימַ ת אַ בֵּּ ל‬ abelian )‫אַ בֵּּ לִ י (ת‬ abelian category ‫קָ טֵּ גו ְֹריָה אַ בֵּּ לִ ית‬ abelian extension ‫הַ ְרחָ בָ ה אַ בֵּּ לִ ית‬ abelian group ... WitrynaThe equivalence of (1) and (4) follows from the fact that being finite locally free is Zariski local on the target (the reference above shows that being finite locally free is in fact … mount pegboard to desk