algebraic geometry, the moduli stack of rank-n vector bundles Vectn is the stack parametrizing vector bundles (or locally free sheaves) of rank n over some reasonable...

"Lectures on the moduli stack of vector bundles on a curve" (PDF), in Schmitt, Alexander (ed.), Affine flag manifolds and principal bundles, Trends in Mathematics...

geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind...

(January 29, 2009), "Lectures on the Moduli Stack of Vector Bundles on a Curve", Affine Flag Manifolds and Principal Bundles, Basel: Springer Basel (published...

{P} (F)} of hyperplanes in F is ample. Several properties of ample line bundles extend to ample vector bundles. For example, a vector bundle F is ample...

closely related moduli stack given by [ A n / G m ] {\displaystyle [\mathbb {A} ^{n}/\mathbb {G} _{m}]} which is the moduli stack of line bundles with n {\displaystyle...

the moduli stack of stable vector bundles on C {\displaystyle C} of rank r {\displaystyle r} and degree d {\displaystyle d} . It has a coarse moduli space...

One of the motivations for analyzing stable vector bundles is their nice behavior in families. In fact, Moduli spaces of stable vector bundles can be...

an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed...

representations of the étale fundamental group of an algebraic curve to objects of the derived category of l-adic sheaves on the moduli stack of vector bundles over...

studying moduli of stable vector bundles in many specific cases, such as on principally polarized abelian varieties and K3 surfaces. A vector bundle E {\displaystyle...

descent implies a vector bundle on Y (so, a bundle given on each Xi), and our concern is to 'glue' those bundles Vi, to make a single bundle V on X. What we...

general linear group; i.e., the moduli stack was the moduli stack of vector bundles, but, today, the term refers to any of generalizations. The scheme-theoretic...

for line bundles on compact Riemann surfaces. Riemann–Roch type theorems relate Euler characteristics of the cohomology of a vector bundle with their...

quasi-projective. Another case is a moduli of vector bundles on a curve. Here, there are the notions of stable and semistable vector bundles on a smooth complete curve...

moduli space of curves. Using the notion of stable vector bundle, coarse moduli schemes for the vector bundles on any smooth complex variety have been...

{\displaystyle \operatorname {Vect} _{n}} denotes the moduli stack of rank-n vector bundles, then there is a presentation Spec ⁡ ( k ) → Vect n {\displaystyle...

good-behaving moduli space of curves. 2.  A stable vector bundle is used to construct the moduli space of vector bundles. stack A stack parametrizes sets of points...

the Hodge bundle, named after W. V. D. Hodge, appears in the study of families of curves, where it provides an invariant in the moduli theory of algebraic...

varieties, proved by Jean-Pierre Serre. The basic version applies to vector bundles on a smooth projective variety, but Alexander Grothendieck found wide...

Lafforgue proved the Langlands conjectures for GLn of a function field by studying the moduli stack of shtukas of rank n. "Shtuka" is a Russian word штука meaning...

{\displaystyle \Gamma ={\text{SL}}_{2}(\mathbb {Z} )} are sections of a line bundle on the moduli stack of elliptic curves. A modular function is a function that...

2022-11-22. Behrend, K. The Lefschetz Trace Formula for the Moduli Stack of Principal Bundles. PhD dissertation. Behrend, Kai; Conrad, Brian; Edidin, Dan;...

can be used to construct the moduli space M C ( n , d ) {\displaystyle {\mathcal {M}}_{C}(n,d)} of semistable vector bundles using a GIT quotient. Hilbert...

determines a morphism of schemes X →Y in a natural way. The Stacks Project, 01J5 The functor of points, Yoneda's lemmma, moduli spaces and universal properties...

representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more...

One can define the moduli stack of principal bundles Bun G ⁡ ( X ) {\displaystyle \operatorname {Bun} _{G}(X)} as the quotient stack [ Ω / G ] {\displaystyle...

language of algebraic geometry, the phase space of the system is a partial compactification of the cotangent bundle to the moduli space of stable G-bundles for...

assume: given an algebraic stack X locally of finite type over a base field k, (homotopy-invariance) if E is a rank-n vector bundle on X, then A p ( E ) =...

Peter Scholze on the stack of vector bundles on the Fargues–Fontaine curve is expected to have implications for the construction of a local Langlands correspondence...