Let $f:X\rightarrow Y$ a morphism between schemes and $Y'\rightarrow Y$ a fpqc morphism such that the base change $f'$ of $f$ to $Y'$ is formally smooth, does it imply that $f$ is …

Denjoy-Carleman classes of differentiable functions, say in Roumieu's form: Given a log-convex sequence $M_n$ of positive number denote by $C_M=C_M(\mathbb{R}^n,0)$ the ring o …

Let a cartesian diagram Let $X'\rightarrow X$ be a rational resolution of singularities of $k$-schemes of finite type and $Y$ a closed subscheme. Let $Y'\rightarrow Y$ be the bas …

Are the Milnor's seven dimensional exotic spheres parallelizable?

Hi, My question is related to Algebraic Surfaces. I have seen that we always consider K3 surfaces which are smooth, but I wonder how can we define a non-smooth K3 surface. The …

Let $\gamma:I\subset\mathbb{R}\rightarrow\mathbb{R}^2, s\mapsto \gamma(s)$, denote the arclength parametrization of a smooth, convex curve $\Gamma:=\gamma(I)\subset\mathbb{R}^2$. E …

Which methods are available for computing a multidimensional integral with Delta distributions (in case one cannot sample them explicitly)? PS: This question correlates with this …

One of the requirements for a smooth manifold $M$ is that it be paracompact, and one of the equivalent definitions of paracompactness for a smooth space is that for overy open cove …

Say I have an ind scheme $X = \cup_i X_i$ over a field $k$. I have its tangent bundle $\hom_k(k[\epsilon], X)$ which I can think of as ind scheme via $\cup_i \hom_k(k[\epsilon],X_i …

Let $[a,b)\subset\mathbb R$, and $F,G:[a,b)\to\mathbb R$ two decreasing piecewise linear functions so that $F(x)\leq G(x)$ for any $x\in[a,b)$. We assume that: there is a numbe …

I have a general question, and then the specific version of that question I need for research. All vector spaces over $\mathbb{C}$. Grassmanians of planes The $(2,n)$-Grassmanni …

I've learned when you have a integral smooth scheme line bundles are the same as Cartier divisors are the same as Weil divisors. My question is to what extent does this continue t …

In the http://arxiv.org/abs/math/0606464v1 I read "If you want to prove existence of exotic smooth structure on $\mathbb R^4$ you can do this if you are in possession of a knot …

Definition. A locally finitely presented morphism of schemes $f\colon X\to Y$ is smooth (resp. unramified, resp. étale) if for any affine scheme $T$, any closed subscheme $T_0$ …

Hello all, could someone point me to a reference that ties the smoothness of the solution $u$ to the classical elliptic problem $\nabla \cdot ( q \nabla u ) = f \;,\; x \in \Omeg …