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  • On the Fundamental Group of a Variety with Quotient Singularities 
    Biswas, Indranil; HOGADI, AMIT (Oxford University Press, 2013-12)
    Let k be a field, and let π:X~⟶X be a proper birational morphism of irreducible k-varieties, where X~ is smooth and X has at worst quotient singularities. When the characteristic of k is zero, a theorem of Kollár [7] says ...
  • On the comparison of two constructions of Witt vectors of non-commutative rings 
    HOGADI, AMIT; PISOLKAR, SUPRIYA (Elsevier B.V., 2018-07)
    Let A be any associative ring, possibly non-commutative and let p be a prime number. Let E(A)be the ring of p-typical Witt vectors as constructed by Cuntz and Deninger in [1] E(A)and be that constructed by Hesselholt in ...
  • Gabber's presentation lemma for finite fields 
    HOGADI, AMIT; KULKARNI, GIRISH (De Gruyter, 2020-02)
    We give a proof of Gabber's presentation lemma for finite fields. We first prove this lemma in the special case of open subsets of the affine plane using ideas from Poonen's proof of Bertini's theorem over finite fields. ...
  • Gabber's presentation lemma over noetherian domains 
    DESHMUKH, NEERAJ; HOGADI, AMIT; KULKARNI, GIRISH; YADAV, SURAJ (Elsevier B.V., 2021-03)
    Following Schmidt and Strunk, we give a proof of Gabber's presentation lemma over a noetherian domain with infinite residue fields.
  • Quasi-Affineness and the 1-Resolution Property 
    DESHMUKH, NEERAJ; HOGADI, AMIT; Mathur, Siddharth (Oxford University Press, 2022-02)
    We prove that, under mild hypothesis, every normal algebraic space that satisfies the 1-resolution property is quasi-affine. More generally, we show that for algebraic stacks satisfying similar hypotheses, the 1-resolution ...
  • Geometric criteria for 𝐴1-connectedness and applications to norm varieties 
    Balwe, Chetan; HOGADI, AMIT; Sawant, Anand (American Mathematical Society, 2023)
    We show that 𝐴1-connectedness of a large class of varieties over a field 𝑘 can be characterized as the condition that their generic point can be connected to a 𝑘-rational point using (not necessarily naive) 𝐴1-homotopies. ...
  • Milnor-Witt cycle modules over an excellent DVR 
    Balwe, Chetan; HOGADI, AMIT; PAWAR, RAKESH (Elsevier B.V., 2023-02)
    The definition of Milnor-Witt cycle modules in [5] can easily be adapted over general regular base schemes. However, there are simple examples (see (2.9)) to show that Gersten complex fails to be exact for cycle modules ...
  • A1-CONNECTEDNESS OF MODULI OF VECTOR BUNDLES ON A CURVE 
    HOGADI, AMIT; Yadav, Suraj (Cambridge University Press, 2023-03)
    In this note, we prove that the moduli stack of vector bundles on a curve with a fixed determinant is A(1)-connected. We obtain this result by classifying vector bundles on a curve up to A(1) concordance. Consequently, we ...
  • Strong A1-invariance of A1-connected components of reductive algebraic groups 
    Balwe, Chetan; HOGADI, AMIT; Sawant, Anand (Wiley, 2023-06)
    We show that the sheaf of A1-connected components of a reductive algebraic group over a perfect field is strongly A1-invariant. As a consequence, torsors under such groups give rise to A1-fiber sequences. We also show that ...
  • Nisnevich local good compactifications 
    Deshmukh, Neeraj; HOGADI, AMIT; Kulkarni, Girish; YADAV, SURAJ  (Springer Nature, 2023-09)
    For a local complete intersection morphism, we establish fibrewise denseness in the n-dimensional irreducible components of the compactification Nisnevich locally.

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