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An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors

100%
Hogadi A., Pisolkar S.
Acta Arithmetica
|
2013
|
tom 158
|
nr 2
165-171
EN
Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension $k_L/k_K$ is separable. For an integer n ≥ 0, let $W_n(𝓞_L)$ denote the ring of Witt vectors of length n with coefficients in $𝓞_L$. We show that the proabelian group ${H^1(G,W_n(𝓞_L))}_{n∈ ℕ}$ is zero. This is an equicharacteristic analogue of Hesselholt's conjecture, which was proved before when the discrete valued fields are of mixed characteristic.
2
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The Brauer group of desingularization of moduli spaces of vector bundles over a curve

81%
Biswas I., Hogadi A., Holla Y.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1300-1305
EN
Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M C (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧r E = L. We show that the Brauer group of any desingularization of M C(r; L) is trivial.
3
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Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

81%
Biswas I., Hogadi A., Holla Y.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1157-1163
EN
Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.
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