Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A necessary condition for liftings of positive characteristic varieties with finite fundamental groups (2506.07914v1)

Published 9 Jun 2025 in math.AT and math.AG

Abstract: In this paper, we introduce a necessary condition for the existence of characteristic zero liftings of certain smooth, proper varieties in positive characteristic, using \'etale homotopy theory and Wall's finiteness obstruction. For a variety with finite \'etale fundamental group pi, we define a notion of mod-l finite dominatedness based on the F_l-chain complex of the universal cover of its l-profinite \'etale homotopy type. We prove that such a variety can be lifted to characteristic zero only if this complex is quasi-isomorphic to a bounded complex of finitely generated projective F_l[pi]$-modules. This extends classical finiteness results in topology to the l-adic and algebro-geometric setting.

Summary

We haven't generated a summary for this paper yet.