All Questions
974 questions with no upvoted or accepted answers
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155
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Siegel's theorem on integral points for higher dimensional varieties
What is know about a generalisation of Siegel's theorem on integral points to higher dimensional varieties?
I found https://books.google.de/books?id=0jt8CwAAQBAJ&pg=PA21&lpg=PA21&dq=...
user19475
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0
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80
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Good cohomological setting for binary operations on arithmetical functions
Is there currently a good abstract theory (derived from algebraic geometry and cohomological theories) to study binary operations on arithmetical functions like the Dirichlet convolution $$f\star g = \...
- 1,017
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236
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Eigenvariety and Hecke algebra
Let $h^{n,ord}(Np^\infty)$ be the cuspidal nearly ordinary Hecke algebra of tame level $N$. For $N \geq 4$, we know that the Hecke algebra is the generic fibre of the Hecke-Hilbert Eigenvariety and so ...
- 1,066
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96
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Fastest algorithm to compute isogeny
Let $E/GF(p)$ and $E'/GF(p')$ are two isogenous elliptic curves($\#E=\#E'$). We know that there exist the map
$$\psi : E \to E'$$
Suppose that we haven't any information about degree of $\psi$.
...
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145
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Lifting points of étale group scheme
Consider the following setting: let $(R,\mathfrak{m})$ be a Noetherian complete discrete valuation ring (with maximal ideal $\mathfrak{m}$) and let $K$ be its field of fractions. Now take $L$ be the ...
- 445
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724
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Extension of a complete discrete valuation ring
My question came when I was reading the famous Tate's paper on $p$-divisible groups. At the beginning of chapter $(2.4)$ he cites this fact as obvious. If you take a complete discrete valuation ring $...
- 445
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95
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Rationality of intersection of algebraic groups
Suppose that $G$ (defined over $\mathbb{Q}$) and $H$ (defined over $\mathbb{R}$) are two algebraic subgroups of a larger algebraic group defined over $\mathbb{Q}$. Assume that $G(\mathbb{R})$ and $H(\...
user70017
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121
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Computing a projection of a $p$-adic plane curve
Given a prime $p$ and a polynomial equation $f(x,y)=0$ with rational coefficients, I would like to obtain a precise description of the set of all numbers $y\in\mathbb Q_p$ such that the equation has a ...
- 1,021
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199
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Question about the "middle" intermediate Jacobian
Suppose $Y$ is a smooth projective variety of dimension $2p-1$ over $\mathbb{C}$. I have a few questions about the $p^{~\text{ th}}$ intermediate Jacobian $J^p(Y)$ of $Y$.
Does it come from (i.e. is ...
- 299
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694
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"Descending cohomology, geometrically" by Mazur:
(Exist texts of that talk or related texts: http://ttv.mit.edu/collections/harris60/videos/13881-problem-session-barry-mazur ?) Article: http://www.math.harvard.edu/~mazur/papers/page37.pdf
- 10.8k
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201
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extending truncated Barsotti-Tate group
Let $X$ be a smooth projective curve defined over a finite field of char $p$, let $G[1]$ be a truncated Barsotti-Tate grop of level-1. My question is : can $G[1]$ be extended to a truncated ...
- 709
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144
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cohomological criterion of triviality
Hi,
let $X$ be a proper curve, not necessarily smooth, but reduced and connected and $E$ a vector bundle on $X$ of rank $r$.
For a line bundle $L$ it is true that the conditions $h^0(X,L)>0$ and ...
- 19
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244
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Uniqueness of decomposition of completely reducible representations
Let $X$ be a smooth, separated scheme of finite type over $\mathbb{F}_q$ where $q=p^r$ for some $r>0$. Let $gcd(l,p)=1, \rho:W(X) \to GL_r(\mathbb{Q}_l)$ be a Weil representation which is semi-...
- 1,070
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373
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Vanishing of motivic cohomology with finite coefficients in negative degrees
I wonder whether the "finite coefficient version" of Beilinson-Soule conjecture i.e. the following statement holds or not.
STATEMENT:
Let $X$ be a smooth and projective scheme over a finite field $\...
- 945
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440
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Foliations in positive characteristic
Ekedahl wrote about foliations in positive characteristic, over the field $\mathbb{Z}/p\mathbb{Z}$ as a subsheaf of the tangent sheaf, that are closed with respect to involution and $p$-power.
My ...
- 1
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82
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Extending functions on curves to functions on abelian varieties
Say I have a function $f_g$ on the moduli space of curves $M_g$ for all $g\geq 1$. Is there some way of extending this to the moduli space of abelian varieties $A_g$ in a nice way?
What if I have ...
- 163
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282
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well known facts on openness condition
Hi,
I would like to understand and prove the following two "well-known" facts:
1)
If $B$ is a scheme and $P$ a property for which I know:
i) if $B=Spec(V)$ where $V$ is a complete DVR, if $P$ ...
- 1
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159
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a question on the Poincar\'e bundle
Let $C$, a smooth curve. Let $J$ its Jacobian, consider the Poincar\'e bundle $\mathcal{P}$ on $J\times J$. Let $p: J\times J\rightarrow J$ the projection.
How can I compute the complex $R p_{*} \...
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148
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Is sum $(E_i, E_j)$ non-positive, with $E_i$'s the exceptional components of a desingularization
Let $Y$ be an integral normal 2-dimensional scheme and let $X\longrightarrow S$ be a flat projective morphism, where $S$ is a Dedekind scheme.
Let $f:X\longrightarrow Y$ be a minimal resolution of ...
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263
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Computing the function field of a curve given as a subvariety of the Jacobian of its cover or merely the degree of the covering
I read following paragraph from:
G. Tamme, Teilkörper höheren Geschlechts eines algebraischen Funktionenkörpers, Arch. Math. 23 (1972), 257--259
Here $C$ is a curve of genus $\ge 2$ and $J$ is the ...
- 601
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352
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Liftability in positive characteristic
What clsses of algebraic varieties over field of positive characteristic can be lift to $W_2(k)$?
- 85
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524
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DeRham cohomology
The Poincare lemma fails in positive characteristic, since pth powers vanish under differention. My question is : is there still some kind of resolution of the local system k by considering some ...
- 1
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253
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A misunderstanding about the Moret Bailly theorem
Sorry for the non-specific title, but this would be hard to fit in one line.
In "Groups as Galois Groups", theorem 10.27 says that there's some absolutely irreducible component of $\mathcal{H}_r^{in}(...
- 5,929
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555
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étale cohomology with values in the $\ell$-torsion of an Abelian scheme
Let $S/\mathbf{F}_q$ be a $d$-dimensional smooth projective variety and $A/S$ be an Abelian scheme. Is there an easy description of $H^0(S, A(\ell)(d-1))$?` ($A(\ell)$ = union of $A_{\ell^n}$)
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