Nikolai Opdan

• Opdan, Nikolai & Hoyois, Marc (2025). Introduction to framed correspondences. The Open Book Series. ISSN 2329-9061. 6(1), p. 107–126. doi: 10.2140/obs.2025.6.107. Full text in Research Archive
• Opdan, Nikolai & Rülling, Kay (2025). Lectures on the cohomology of reciprocity sheaves. The Open Book Series. ISSN 2329-9061. 6(1), p. 127–163. doi: 10.2140/obs.2025.6.127. Full text in Research Archive

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• Opdan, Nikolai (2025). Three Perspectives on Logarithmic Motivic Spectra. Universitetet i Oslo. Full text in Research Archive Show summary

  Motivic homotopy theory, developed by Morel and Voevodsky in the 1990s, transfers ideas from algebraic topology to algebraic geometry and led to landmark results such as Voevodsky’s proofs of the Milnor and Bloch–Kato conjectures. Classical motivic homotopy theory identifies two objects if they can be connected via the affine line. While effective in many cases, it does not capture important phenomena arising from singularities or degenerations. Logarithmic geometry, introduced by Kato, Fontaine, and Illusie, provides a natural framework to study these subtler situations. Building on this, Binda, Park, and Østvær developed logarithmic motivic homotopy theory, replacing the affine line with its logarithmic compactification. Within this context, my work provides two new descriptions of logarithmic motivic spectra, equipping them with improved categorical properties. I also develop logarithmic versions of the h- and v-topologies for logarithmic schemes and prove that the log étale cohomology satisfies descent. This allows motivic methods to be applied to the étale topology with torsion coefficients in positive characteristic and suggests a method for defining logarithmic motives over log points.

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