Nilay Kumar
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 Jan6 comment Defining a sheaf of differential operators Actually, I'm not sure I understand why those two are the same for basis opens... sorry for for being so confused! It seems to me that the first should be much larger, as its sections on U need not be ad-nilpotent (on $U$), which is not true for the latter. Jan6 comment Defining a sheaf of differential operators I'm a bit confused what with all the open sets flying about, so let me try to be more precise. Let $U$ be open, and $\{U_i\}$ an open cover, with $s_i$ on $U_i$ compatible and ad-nilpotent above $U_i\cap V$, $V$ any basis open. We obtain $s$ on $U$ restricting to $s_i$ from the sheaf-ness of $\mathscr{H}$; it remains to check that $s$ is ad-nilpotent above $U\cap V$, $V$ any basis open. But I don't think this follows immediately from sections on [$U\cap V$] are precisely those that live in ... for each $i$,'' as the $U_i$ that we are additionally restricting to are not arbitrary basis opens. Jan4 comment Defining a sheaf of differential operators The obvious thing to do would be to use the sheaf condition on $\mathcal{N}$ together with the commutativity of some diagram to conclude that ad action by any $\max_{i\in I} k_i$ functions on $s$ yields 0, where the $k_i$ are the orders of the $s_i$. Unfortunately, this $\max_{i\in I} k_i$ is not well-defined -- the open cover might yield sections with orders following an infinite arithmetic progression. Does (quasi-)coherence of $\mathcal{M}$,$\mathcal{N}$ come into play? Or is there something that I'm missing? Jan4 comment Defining a sheaf of differential operators This cleared up a lot of things, thanks! One remaining question I have is the following. In proving that $\operatorname{Diff}(\mathcal{M},\mathcal{N})$ is a subsheaf of $\operatorname{\mathscr{H}\!om}_\mathbb{C}(\mathcal{M},\mathcal{N})$ one needs to show (more or less) that derivations $s_i$ over restrictions $V_i$ glue to a derivation $s$ over $V$ (for $V$ open affine, say). The sheaf condition on $\mathscr{H}$ yields a homomorphism that restricts to the $s_i$, but how does one show that there exists $k$ such that for any $k+1$ functions, repeated ad action on $s$ yields 0? Jan3 accepted Defining a sheaf of differential operators Jan2 asked Defining a sheaf of differential operators Jun11 revised Explicit Weierstrass Preparation Theorem decomposition added relevant tags Jun9 accepted Is the zero set of a holomorphic function nowhere dense? Jun9 comment Is the zero set of a holomorphic function nowhere dense? Oh, of course! Well that was very silly of me -- thanks! Jun9 asked Explicit Weierstrass Preparation Theorem decomposition Jun9 asked Is the zero set of a holomorphic function nowhere dense? Mar23 revised Closed orbits of complete flags in $\mathbb{C}^n$ edited tags Mar12 revised $\dim (A/I) \le \dim (A)$ added a reference Mar12 answered $\dim (A/I) \le \dim (A)$ Mar12 asked Closed orbits of complete flags in $\mathbb{C}^n$ Jan4 comment Finding frame bundles What exactly do you mean by 'finding' a frame bundle? Isn't a frame bundle just the a principal G-bundle where the fiber over $x\in M$ is isomorphic to the group of (orthogonal in the Riemannian case) frames at $P_x$? Sep11 awarded Enthusiast Aug29 answered Partial derivatives, don't know how to solve it Aug27 awarded Citizen Patrol Aug27 revised Find all intermediate fields of extension $\mathbb{Q}(\sqrt{2} , \sqrt{3}) : \mathbb{Q}$ without using Galois correspondence. Minor typos