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Angelo
  • Member for 14 years, 9 months
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Are all representations of $G\times H$ induced from representations of $G$ and $H$?
added 142 characters in body; added 213 characters in body
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notion of torsor defined by exact sequence
The torsor is the inverse image of 1 in $N$.
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Tensor product of lattices
Your question is off-topic here, as this website is for research level math questions. I suggest trying at math.stackexchange.com .
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Deforming to decompose vector bundles
Yes, it is true over curves.
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Deforming to decompose vector bundles
No, this is false, a vector bundle can be indecomposable for simple numerical reason, i.e., because the Chern polynomial is not a product of linear factors (think of the tangent bundle to $\mathbb P^2$); deforming it does not change the Chern polynomial.
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open immersion between affine spaces
For the second part, it is easier to spread on a finitely generated domain, then count points in fibers.
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Accessible problems on classical groups over complex or real numbers.
Usually, in undergraduate research, coming up with problems is part of the professor's job, not the student's.
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When is the intersection of an isolated normal singularity with a generic linear subspace through that singularity normal?
Actually, the way the question was formulated so that the intersection has dimension 2. In this case, to get a positive answer you need the singularity to be Cohen-Macaulay.
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Embedded associated prime and non zero divisor
If you can't do your homework problems, I would suggest, first of all, studying, and, if this fails, going to your teacher's office hours. I voted to close.
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Flatness over Jacboson ring
No. Take $A = k[x,y]$, and as $M$ the quotient field of $k[x] = k[x,y]/(y)$.
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Simple automorphism groups of field extensions of infinite transcendence degree
I suppose you want $k$ to be also algebraically closed, otherwise the subgroup of elements fixing $\overline k \subseteq K$ would be a proper normal subgroup. I don't have access to Lascar's paper, but from the title I would guess he takes $k = \overline{\mathbb Q}$.
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Proving that a generic variety with ample canonical bundle has no automorphisms
I meant this: it is very hard to imagine this might be true, but if it were, it would probably be extremely difficult to prove. In any case, it seems that you are being given counterexamples.
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