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<p>We give a formula for the essential dimension of a cohomology class <i>α</i> in <i>H</i><sup><i>d</i></sup>(<i>K</i>, ℚ<sub><i>p</i></sub>/ℤ<sub><i>p</i></sub>(<i>d</i>)) when <i>K</i> is a strictly Henselian field. This formula is particularly explicit in the case where <i>α</i> is a Brauer class (for <i>d</i> = 2). As an application of our bound with <i>d</i> = 3, we study the essential dimension of exceptional groups by examining the image of the Rost invariant.</p>

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Essential dimension of cohomology classes via valuation theory

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Danny Ofek,
  • Zinovy Reichstein

摘要

We give a formula for the essential dimension of a cohomology class α in Hd(K, ℚp/ℤp(d)) when K is a strictly Henselian field. This formula is particularly explicit in the case where α is a Brauer class (for d = 2). As an application of our bound with d = 3, we study the essential dimension of exceptional groups by examining the image of the Rost invariant.