What does this research mean for the field?

The maximal dimension of a subspace of the generic tensor product of symbol algebras of prime degree is bounded by a specific formula. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine the maximal dimension of a subspace of generic tensor products of symbol algebras with vanishing characteristic coefficients.

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February 28, 2026

Spaces with Vanishing Characteristic Coefficients

Key Points

To determine the maximal dimension of a subspace of generic tensor products of symbol algebras with vanishing characteristic coefficients.
Proved dimension limits for subspaces of generic tensor products of prime degree symbol algebras.
Utilized properties of subsets in relation to characteristic coefficients.
Showed relationships between specific elements within the algebra structure.
Established an upper bound for subspace dimensions in terms of vanishing coefficients.
Confirmed dimension limits across different configurations of the tensors.
Showed consistent outcomes regardless of the characteristic coefficients being zero.

Abstract

We prove that the maximal dimension of a subspace Formula: see text of the generic tensor product of Formula: see text symbol algebras of prime degree Formula: see text with Formula: see text for all Formula: see text is Formula: see text. The same upper bound is thus obtained for Formula: see text with Formula: see text, Formula: see text, Formula: see text, Formula: see text being 0 for all Formula: see text. We make use of the fact that given any subset Formula: see text of Formula: see text (Formula: see text times) with Formula: see text, for all Formula: see text there exist Formula: see text, Formula: see text in Formula: see text and Formula: see text in Formula: see text such that Formula: see text.

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Spaces with Vanishing Characteristic Coefficients

Key Points

Abstract

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