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Blow-up invariance of cohomology theories with modulus
Junnosuke Koizumi
In this paper, we study cohomology theories of -modulus pairs, which are pairs consisting of a scheme and a -divisor . Our main theorem prov…
A motivic construction of the de Rham-Witt complex
Junnosuke Koizumi, Hiroyasu Miyazaki
The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs of a variety and a…
Transfers on commutative group schemes
Junnosuke Koizumi
We prove that any commutative group scheme separated over a noetherian normal scheme admits a canonical structure of a presheaf with transfers, which is characterized by a simple c…
Steinberg symbols and reciprocity sheaves
Junnosuke Koizumi
We study multilinear symbols on fields taking values in reciprocity sheaves. We prove that any such symbol satisfying natural axioms automatically has Steinberg-type relations, whi…
Zeroth -homology of smooth proper varieties
Junnosuke Koizumi
We give an explicit formula for the zeroth -homology sheaf of a smooth proper variety. We also provide a simple proof of a theorem of Kahn-Sujatha which describes hom…