39 research outputs found
Density of Arithmetic Representations of Function Fields
No full textWe propose a conjecture on the density of arithmetic points in thedeformation space of representations of the \'etale fundamental group inpositive characteristic. This? conjecture has applications to \'etalecohomology theory, for example it implies a Hard Lefschetz conjecture. We provethe density conjecture in tame degree two for the curve . v2: very small typos corrected.v3: final. Publication inEpiga.Comment: 18 page
The Gersten conjecture for Milnor K-theory
No full textWe prove that the n-th Milnor K-group of an essentially smooth local ring over an infinite field coincides with the (n,n)-motivic cohomology of the ring. This implies Levine's generalized Bloch-Kato conjecture
Milnor K-theory and motivic cohomology
No full textThese are the notes of a talk given at the Oberwolfach Workshop K-Theory 2007. We sketch a proof of Beilinson’s conjecture relating Milnor K-theory and motivic cohomology. For detailed proofs see [4]
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Algebraic K-theory
No full textAlgebraic -theory has seen a fruitful development during the last three
years. Part of this recent progress was driven by the use of -categories and
related techniques originally developed in algebraic topology. On the other hand we have
seen continuing progress based on motivic homotopy theory which has been an important
theme in relation to
algebraic -theory for twenty years
Milnor K-theory of local rings
No full textWe prove a conjecture of Beilinson and Lichtenbaum which predicts the existence of an isomorphism between Milnor K-theory and motivic cohomology of local rings
Milnor 𝐾-theory of local rings with finite residue fields
No full textWe propose a definition of improved Milnor
K
K
-groups of local rings with finite residue fields, such that the improved Milnor
K
K
-sheaf in the Zariski topology is a universal extension of the naive Milnor
K
K
-sheaf with a certain transfer map for étale extensions of local rings. The main theorem states that the improved Milnor
K
K
-ring is generated by elements of degree one.</p
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Algebraic K-Theory
No full textAlgebraic -theory has seen further progress during the last three years. One important aspect of this recent progress has been a better conceptual understanding of motivic filtrations on -theory and the systematic use of localizing invariants and related concepts. Progress on motivic cohomology has also played an important role concerning foundations as well as applications
