6 citations · 19 across the 12 of their papers we have counts for
13 papers · 1 filter
Transfers on -connected components of quasi-split groups and the norm principle
Amit Hogadi, Anand Sawant
We show that the sheaf of -connected components of a quasi-split group over a perfect field is a strictly -invariant sheaf with (Voevodsky) transfers. As…
Tame and curve-tame cohomology of -invariant étale sheaves
Sandeep S, Anand Sawant
We extend the definition of the unramified curve-tame cohomology groups to -invariant étale sheaves under some additional hypotheses. We define a pairing of this grou…
Strong -invariance of -connected components of reductive algebraic groups
Chetan Balwe, Amit Hogadi, Anand Sawant
We show that the sheaf of -connected components of a reductive algebraic group over a perfect field is strongly -invariant. As a consequence, torsors unde…
Remarks on iterations of the -chain connected components construction
Chetan Balwe, Bandna Rani, Anand Sawant
We show that the sheaf of -connected components of a Nisnevich sheaf of sets and its universal -invariant quotient (obtained by iterating the $\mathbb A^1…
Geometric criteria for -connectedness and applications to norm varieties
Chetan Balwe, Amit Hogadi, Anand Sawant
We show that -connectedness of a large class of varieties over a field can be characterized as the condition that their generic point can be connected to a -rat…
Cellular -homology and the motivic version of Matsumoto's theorem
Fabien Morel, Anand Sawant
We define a new version of -homology, called cellular -homology, for smooth schemes over a field that admit an increasing filtration by open subschemes wi…
Naive -homotopies on ruled surfaces
Chetan Balwe, Anand Sawant
We explicitly describe the -chain homotopy classes of morphisms from a smooth henselian local scheme into a smooth projective surface, which is birationally ruled over…
A^1-connected components of ruled surfaces
Chetan Balwe, Anand Sawant
A conjecture of Morel asserts that the sheaf of -connected components of a space is -invariant. Using purely algebro-geometric methods, we determine the s…
Rost nilpotence and étale motivic cohomology
Andreas Rosenschon, Anand Sawant
A smooth projective scheme over a field is said to satisfy the Rost nilpotence principle if any endomorphism of in the category of Chow motives that vanishes on an exte…
Naive vs. genuine A^1-connectedness
Anand Sawant
We show that the triviality of sections of the sheaf of A^1-chain connected components of a space over finitely generated separable field extensions of the base field is not suffic…
A^1-connectedness in reductive algebraic groups
Chetan Balwe, Anand Sawant
Using sheaves of A^1-connected components, we prove that the Morel-Voevodsky singular construction on a reductive algebraic group fails to be A^1-local if the group does not satisf…
R-equivalence and A^1-connectedness in anisotropic groups
Chetan Balwe, Anand Sawant
We show that if G is an anisotropic, semisimple, absolutely almost simple, simply connected group over a field k, then two elements of G over any field extension of k are R-equival…
A^1-connected components of schemes
Chetan Balwe, Amit Hogadi, Anand Sawant
A conjecture of Morel asserts that the sheaf of A^1-connected components of a simplicial sheaf X is A^1-invariant. A conjecture of Asok-Morel asserts that A^1-connected components…