prochet

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Name	prochet
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15h	comment	Smooth map to the stack of G-bundles very enlightening thank you!
1d	asked	lift elements in affine singular variety.
2d	comment	descent for formally smooth maps In the infinitesimal lifting property, can we reduce to easier rings, such local henselian or local for example?
Jun 16	asked	descent for formally smooth maps
Jun 14	comment	Smooth map to the stack of G-bundles In my case, $Bun_{B,r}$ corresponds to the open substack obtained by base change from the analog open substack $\Bun_{T,r}$ consisting of $T$-torsors E such that $H^{1}(X,E\times^{T}V)=0$ for any representation $V$ of $T$ which appear as subquotients of $Lie(U^{-})$ where $U^{-}$ is the opposite unipotent radical of $B$
Jun 13	comment	Smooth map to the stack of G-bundles I don't understand the purpose of the lemma 14.2.1 then, why restricting to an open subset if everything is already smooth with connected fibers?
Jun 12	asked	Smooth map to the stack of G-bundles
Jun 12	comment	differential of the characteristic polynomial For example if $F=k((\pi))$ and $\mathcal{O}=k[[\pi]]$ do we have that for $n$ big enough an section $h\in\mathfrak{g}(X-x)$ such that: $d\chi_{\gamma}(h)=\pi^{-n}\mathcal{O}^{*}+Q(\pi^{-1})$ with $Q$ a polynomial of degree less than n-1?
Jun 12	comment	differential of the characteristic polynomial $k$ an algebraically closed field.
Jun 12	comment	differential of the characteristic polynomial the motivation is the following: Let $F$ a local field at a closed point $x$ of a smooth projective curve $X$ over $k$ (completion of function field at the place $x$). I take $\gamma\in G(F)$ regular semsisimple, we then have a map $d\chi_{\gamma}:\mathfrak{g}(F)\rightarrow \mathbb{A}^{r}(F)$ my question is to try to characterize the image of $d\chi_{\gamma}(\mathfrak{g}(X-x))$ where $\mathfrak{g}(X-x)$ denotes the section of $\mathfrak{g}$ with values in $X-x$.
Jun 11	asked	differential of the characteristic polynomial
Jun 8	comment	Galois cohomology of the field of Laurent series or at least do we have that any $T$-torsor on $k((t))$ is trivial? As a matter of fact I think that $k((t))$ is of cohomological dimension one only if $k$ is algebraically closed.
Jun 8	asked	Galois cohomology of the field of Laurent series
Jun 8	comment	closed subscheme of ind scheme yes, that's right.
Jun 8	comment	closed subscheme of ind scheme maybe we also need to assume that $X$ is a indscheme over a countable set.
Jun 8	asked	closed subscheme of ind scheme
Jun 6	asked	open immersion, affine grassmanian and negative loop group
May 29	asked	etale cohomology of an abelian variety and its dual
May 25	asked	open immersion between affine spaces
May 19	asked	affine schubert cells and bruhat order
May 17	asked	affine weyl group and affine schubert cells
May 14	comment	weights and exceptional root systems thanks a lot for your detailed answer.
May 13	comment	weights and exceptional root systems It doesn't always hold, because in case $D_{n}$ it never holds, but maybe there is sth that I don't understand in your answer?
May 13	asked	weights and exceptional root systems
May 13	awarded	● Supporter
May 10	comment	solve the singularities of parabolic orbits of schubert cells yes but a resolution of singularities of $\overline{BwP}$ is birational on $BwP$ and not on $PwP$ a priori
May 10	asked	solve the singularities of parabolic orbits of schubert cells
May 7	comment	quasi-minuscule representations And for these representations, what is the characteristic polynomial? More generally where can we find the polynomial invariants for exceptional groups?
May 7	comment	quasi-minuscule representations yes but we don't know to which highest weight they correspond.
May 7	asked	quasi-minuscule representations
May 6	comment	group generated by Coxeter elements How do we know that they generate a normal subgroup? And for $C_{2n+1}$ or $B_{2n+1}$ do we still obtain W?
May 5	asked	group generated by Coxeter elements
Apr 16	comment	The intersection complex and the Cohen-Macaulay property d is the codimension, IC is the intersection complex.
Apr 15	comment	The intersection complex and the Cohen-Macaulay property Let assume also that both X and Y are equidimensionnal, and that a resolution of singularities for X gives by base change a resolution of singularities for Y.
Apr 15	asked	The intersection complex and the Cohen-Macaulay property
Apr 14	asked	on flat morphisms
Apr 13	asked	on rational singularities
Apr 12	asked	semicontinuity results for weights
Apr 6	comment	sections of vector bundles transversal to a divisor I mean that for a point $x\in X$ and $s$ a section of $E$, either $x\in S$ and the $s(x)\notin D$, either $x\in X-S$ and then s(x) needs to meet transversally $D$.
Apr 4	asked	sections of vector bundles transversal to a divisor
Mar 20	asked	on geometric Satake and functions
Feb 19	asked	on degree zero elements in adelic groups
Feb 14	asked	on z-extensions
Feb 13	comment	sections of vector bundles Yes I shouldn't have formulate like this. In fact, I only need the proposition for $V'\subset V$ two vector spaces such that $E$ (resp E') are the trivial vector bundles of fibres V and V'
Feb 13	asked	sections of vector bundles
Feb 9	comment	minuscule representations and classical groups I stated for classical groups to make the statement easier, because although $E_{6}$ and $E_{7}$ have minuscule weights, $E_{8}$ $F_{4}$ and $G_{2}$ don't. Moreover, I know that groups don't have to be simply connected to have minuscule weights or coweights, because in my comment I took the example of $GL_{n}$. Nevertheless, if I take $SL_{n}$ for example, it doesn't have minuscule coweights, so my question was, is it possible to have a $z$-extension of $SL_{n}$, for example, that admits minuscule coweights.
Feb 8	comment	on trivialisation of T-torsors $x$ is a closed point on the curve
Feb 8	comment	minuscule representations and classical groups and in fact, my question is rather for minuscule coweights,
Feb 8	comment	minuscule representations and classical groups the comment is in two part, the example is to answer your second question. I used classical types, because we now that in each type, the simply connected group associated to it has at least one minuscule representations. For exceptional type, a group of type $G_{2}$ doesn't have minuscule representations.
Feb 8	comment	minuscule representations and classical groups I restrict for classical groups, because for exceptional types, there is not minuscule weights. For instance, if I take $PGL_{n}$ there is no minuscule irréducible representations, but for $GL_{n}$ yes

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