I was wondering how much of the theory say of Lazarsfeld books can be carried to algebraic stacks (if this has been done). Do we have a sensible notion of ample (big, nef) line bu …

I was wondering if there is any general theorem, which guarantees the flatness of $\omega_{X/B}$ over $B$ for a flat morphism $f : X \to B$ of schemes of finite type over $\mathbb{ …

Yet another question of the form 'How to apply the decomposition theorem?' The example that I am considering ought to have a simple answer, but I'm getting confused and I would app …

I am currently doing a self study on Algebraic geometry but my ultimate goal is to study more on elliptic curves. Which are the most recommended textbooks I can use to study? I nee …

I can't really say that I understand what a weight is, but the qualitative distinction between weight zero and positive weight has come up a couple times in MathOverflow questions: …

Let $X/K$ be a variety over a global field $K$. When (and why) is the Galois representation $H^i_{et}(X \times_K \bar{K}, \mathbf{Q}_\ell)$ unramified at a place $v$ of $K$? I gue …

A couple weeks ago I attended a talk about the Keel-Mori theorem regarding existence of coarse moduli spaces for Deligne-Mumford stacks with finite inertia. Here are some questions …

This question is perhaps somewhat soft, but I'm hoping that someone could provide a useful heuristic. My interest in this question mainly concerns various derived equivalences aris …

Set-up for classical Springer Correspondence: $G$ = reductive group over $\mathbb{C}$, with Borel subgroup and maximal torus $B \supset T$, Weyl group $W=N_G(T)/T$. Fix a unipote …

Hartshorne EX I 3.18 b Define a curve by [t^4,t^3s,ts^3,s^4]. It is actually a P^1. Why the curve [t^4,t^3s,ts^3,s^4] is not projectively normal in P^3?

Let $E$ be your favorite elliptic curve, and let $Tor^m$ be the moduli stack of torsion sheaves of degree $m$ on $E$. This sounds horrible, but it's not so bad; it's a global quot …

Hello, this one has always been mysterious to me. The Kähler differentials $\Omega_{A/k}$ are definined, by the universal property $$Der_k(A,M)=A-Mod(\Omega_{A/k},M)$$ so for $M=A …

Let $X$ be a nice variety over $\mathbb{C}$, where nice probably means smooth and proper. I want to know: How can we show that the hypercohomology of the algebraic de Rham complex …

Why don't we stay at D-module on base affine space but go to study flag variety of Lie algebra? I remembered there are nice papers of Bernstein-Gelfand-Gelfand and Gelfand-Kirillo …

Suppose I have a compact Riemann surface of $g>1$ given by the quotient $H/\Gamma$ where I do know $\Gamma$ explicit. Is there a way to write down the power series of meromorphic f …