2 problems

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Existence conjecture for Ulrich modules over Cohen–Macaulay local rings
Ulrich module existence conjecture. Ulrich modules exist over every Cohen–Macaulay local ring $R$ .
Conjectureopencohen-macaulay-rings commutative-algebra ulrich-modulesarXiv posted 2 days ago
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The Ext-module conjecture for standard determinantal schemes
Ext-module conjecture. For every integer $i$ with $0\leq i\leq c$ , the module
Conjectureopendeterminantal-varieties maximal-cohen-macaulay-modules ulrich-modulesarXiv posted 2 days ago

Existence conjecture for Ulrich modules over Cohen–Macaulay local rings